Vol.5. Integrals and Series: elementary functions

Integrals and Series Vol.1 - Elementary Functions(1992)
	Contents
	Preface
	Chapter 1. Indefinite Integrals
		1.1 Introduction
		1.2 The Power and Algebraic Functions
		1.3 The Exponential Function
		1.4 Hyperbolic Functions
		1.5 Trigonometric Functions
		1.6 The Logarithmic Function
		1.7 Inverse Trigonometric Functions
	Chapter 2. Definite Integrals
		2.1 Introduction
		2.2 The Power and Algebraic Functions
		2.3 The Exponential Function
		2.4 Hyperbolic Functions
		2.5 Trigonometric Functions
		2.6 The Logarithmic Function
		2.7 Inverse Trigonometric Functions
		2.8 Inverse Hyperbolic Functions
	Chapter 3. Multiple Integrals
		3.1 Double Integrals
		3.2 Triple Integrals
		3.3 Multiple Integrals
	Chapter 4. Finite Sums
		4.1 Introduction
		4.2 Binomial Coefficients
		4.3 Hyperbolic Functions
		4.4 Trigonometric Functions
	Chapter 5. Series
		5.1 Numerical Series
		5.2 Power Series
		5.3 Series Involving the Exponential and Hyperbolic Functions
		5.4 Trigonometric Series
		5.5 Series Involving the Logarithmic and Inverse Trigonometric Functions
	Chapter 6. Products
		6.1 Finite Products
		6.2 Infinite Products
	Appendix I. Some Elementary Functions and their Properties
		I.1 Trigonometric Functions
		I.2 Hyperbolic Functions
		I.3 Inverse Trigonometric Functions
		I.4 Inverse Hyperbolic Functions
		I.5 Binomial Coefficients
		I.6 The Pochhammer Symbol (a)_k
	Appendix II. Some Special Functions and their Properties
		II.1 The Gamma Function Γ(z)
		II.2 The Function ψ(z)
		II.3 The Function β(z)
		II.4 The Riemann Zeta Function ζ(z)
		II.5 The Bernoulli Polynomials B_n(x)
		II.6 The Bernoulli Numbers B_n
		II.7 The Euler Polynomials E_n(x)
		II.8 The Euler Numbers E_n
	Appendix III. Table of the Functions V_i and V_i^±
	Bibliography
		[18]
	Additional References
		[4]
		[33]
	Index of Notations for Functions and Constants
	Index of Mathematical Symbols
	Index of Series Expansions of Some Functions
	Index of Integral Representations of Some Special Functions in Terms of Elementary Functions
Integrals and Series Vol.2 - Special Functions(1992)
	Contents
	Preface
	Chapter 1. Indefinite Integrals
		1.1 Introduction
		1.2 The Incomplete Gamma Functions γ(α,x) Γ(α,x) and Beta Function B_x(α,β)
		1.3 The Exponential Integral Ei(x)
		1.4 The Sine and Cosine Integrals si(x) and ci(x)
		1.5 The Error Functions erf(x), erfc(x)
		1.6 The Fresnel Integrals S(x) and C(x)
		1.7 The Parabolic-Cylinder Function D_ν(x)
		1.8 The Bessel Function J_ν(x)
		1.9 The Neumann Function Y_ν(x)
		1.10 The Hankel Functions H^{(1)}_ν(x) and H^{(2)}_ν(x)
		1.11 The Modified Bessel Function I_ν(x)
		1.12 The Macdonald Function K_ν(x)
		1.13 The Cylindrical Functions Z_ν(x)
		1.14. The Orthogonal Polynomials of Legendre P_n(x), Chebyshev T_n(x), U_n(x), Laguerre L_n(x), L^α_n(x), Hermite H_n(x), Gegenbauer C^ν_n(x), and Jacobi P^{(α,β}_n(x)
	Chapter 2. Definite Integrals
		2.1 Introduction
		2.2 The Gamma Function Γ(x)
		2.3 The Psi Function ψ(x)
		2.4 The Riemann Zeta Function ζ(x)
		2.5 The Exponential Integral Ei(x)
		2.6 The Sine and Cosine Integrals si(x) and ci(x)
		2.7 The Hyperbolic Sine and Cosine Integrals shi(x) and chi(x)
		2.8 The Error Functions erf(x) and erfc(x)
		2.9 The Fresnel Integrals S(x) and C(x)
		2.10 The Incomplete Gamma Functions Γ(ν,x) and γ(ν,x)
		2.11 The Parabolic-Cylinder Function D_ν(x)
		2.12 The Bessel Function J_ν(x)
		2.13 The Neumann Function Y_ν(x)
		2.14 The Hankel Functions H^{(1)}_ν(x) and H^{(2)}_ν(x)
		2.15 The Modified Bessel Function I_ν(x)
		2.16 The Macdonald Function K_ν(x)
		2.17 The Legendre Polynomials P_n(x)
		2.18 The Chebyshev Polynomials T_n(x) and U_n(x)
		2.19 The Laguerre Polynomials L^λ_n(x)
		2.20 The Hermite Polynomials H_n(x)
		2.21 The Gegenbauer Polynomials C^λ_n(x)
		2.22 The Jacobi Polynomials P^{(ρ,σ)}_n(x)
	Chapter 3. Multiple Integrals
		3.1 Introduction
		3.2 Double Integrals
		3.3 Triple Integrals
		3.4 Multidimensional Integrals
	Chapter 4. Finite Sums
		4.1 Introduction
		4.2 The Bessel Functions J_ν(z), I_ν(z), Neumann Function Y_ν(z), and Macdonald Function J_ν(z)
		4.3 The Legendre Polynomials P_n(x)
		4.4 The Laguerre Polynomials L^α_n(x)
		4.5 The Hermite Polynomials H_n(x)
		4.6 The Gegenbauer Polynomials C^λ_n(x)
		4.7 The Jacobi Polynomials P^{(α,β)}_n(x)
	Chapter 5. Series
		5.1 Introduction
		5.2 The Incomplete Gamma Functions γ(α,x), Γ(α,x)
		5.3 The Riemann Zeta Function ζ(z)
		5.4 The Sine and Cosine Integrals Si(x) and ci(x)
		5.5 The Error Functions erf(x), erfi(x)
		5.6 The Parabolic-Cylinder Function D_ν(x)
		5.7 The Bessel Function J_ν(z)
		5.8 The Modified Bessel Function I_ν(z)
		5.9 Various Series Containing the Bessel Functions J_ν(z), I_ν(z), Neumann Function Y_ν(z), and Macdonald Function K_ν(z)
		5.10 The Legendre Polynomials P_n(x)
		5.11 The Laguerre Polynomials L^α_n(x)
		5.12 The Hermite Polynomials H_n(x)
		5.13 The Gegenbauer polynomials C^ν_n(x)
		5.14 The Jacobi Polynomials P^{(α,β)}_n(x)
	Appendix I. The Binomial Coefficients (a b) and the Pochhammer Symbol (a)_k
		I.1 The binomial coefficients (a b)
		I.2 The Pochhammer symbol (a)_k
	Appendix II. Some Special Functions and Their Properties
		II.1 The gamma function Γ(z)
		II.2 The beta function B(a,b)
		II.3 The psi function ψ(z)
		II.4 The Riemann zeta function ζ(z) and ζ(z,v)
		II.5 The exponential integral Ei(z), sine integrals si(z), Si(z), shi(z) and cosine integrals ci(z), chi(z)
		II.6 The error functions erf(z), erfc(z), erfi(z) and Fresnel integrals S(z), C(z), S(z,v), C(z,v)
		II.7 The incomplete gamma functions γ(ν,z), Γ(ν,z)
		II.8 The parabolic-cylinder function D_ν(z)
		II.9 The Bessel function J_ν(z), Neumann function Y_ν(z), and Hankel function H^{(1)}_ν(z), H^{(2)}_ν(z)
		II.10 The modified Bessel function I_ν(z) and Macdonald function K_ν(z)
		II.11 The orthogonal polynomials of Legendre P_n(z), Chebyshev T_n(z), U_n(z), Laguerre L_n(z), L^γ_n(z), Hermite H_n(z), Gegenbauer C^λ_n, and Jacobi P^{(τ,σ)}_n(z)
	Bibliography
		[21]
	Index of notations for functions and constants
	Index of mathematical symbols
Integrals and Series Vol.3 - More Special Functions(1986)
	Contents
	Preface
	Chapter 1. Indefinite Integrals
		1.1 Introduction
		1.2 The Generalized Zeta Function ζ(s,x), Bernoulli Polynomials B _n (x), Euler Polynomial E_n(x) and Polylogarithms Li_ν(x)
		1.3 The Generalized Fresnel Integrals S(x,ν) and C(x,ν)
		1.4 The Struve Functions H_ν(x) and L_ν(x)
		1.5 The Anger Function J_ν(x) and Weber Function E_ν(x)
		1.6 The Lommel Functions s_{μ,ν}(x) and S_{μ,ν}(x)
		1.7 The Kelvin Functions ber_ν(x), bei_ν(x), ker_ν(x) and kei_ν(x)
		1.8 The Airy Functions(x) and Bi(x)
		1.9 The Integral Functions of Bessel Ji_ν(x), Neumann Yi_ν(x) and MacDonald  Ki_ν(x)
		1.10 The Incomplete Elliptic Integrals F(x,k), E(x,k) and Π(x,ν,k)
		1.11 The Complete Elliptic Integrals K(k), E(k) and Π(π/2,ν,k)
		1.12 The Legendre Functions P^μ_ν(x) and Q^μ_ν(x)
		1.13 The Whittaker Functions M_{ρ,σ}(x) and W_{ρ,σ}(x)
		1.14 The Confluent Hypergeometric Functions of Kummer _1F_1(a; b; x) and Tricomi ψ(a,b ; x)
		1.15 The Gauss Hypergeometric Function _2F_1(a, b; c; x)
		1.16 The Generalized Hypergeometric Function _pF_q((a_p); (b_q); x), the Meijer G-Function, the MacRobert E-Function and the Fox H-Function
		1.17 The Elliptic Functions of Jacobi and Weierstrass
	Chapter 2. Definite Integrals
		2.1 Introduction
		2.2 The Gamma Function Γ(x)
		2.3 The Generalized Zeta Function ζ(s,x)
		2.4 The Polynomials of Bernoulli B_n(x) and Euler E_n(x)
		2.5 The Polylogarithm Li_ν(x)
		2.6 The Generalized Fresnel Integrals S(x,ν) and C(x,ν)
		2.7 The Struve Functions H_ν(x) and L_ν(x)
		2.8 The functions of Anger J_ν(x) and Weber E_ν(x)
		2.9 The Lommel Functions s_{µ,ν}(x) and S_{µ,ν}(x)
		2.10 The Kelvin Functions {ber_ν(x) bei_ν(x)} and {ker_ν(x) kei_ν(x)}
		2.11 The Airy Functions Ai(x) and Bi(x)
		2.12 The Integral Functions of Bessel Ji_ν(x), Neumann Yi_ν(x) and MacDonald Ki_ν(x)
		2.13 The Laguerre Function L_ν(x)
		2.14 The Bateman Function k_ν(x)
		2.15 The Incomplete Elliptic Integrals F(x,k), E(x,k), Π(x,ν,k)
		2.16 The Complete Elliptic Integrals K(x), E(x)
		2.17 The Legendre Function of the 1st Kind P_ν(x), P^μ_ν(x)
		2.18 The Legendre Functions of the 2nd Kind Q_ν(x), Q^μ_ν(x)
		2.19 The Whittaker Functions M_{ρ,σ}(x) and W_{ρ,σ}(x)
		2.20 The Confluent Hypergeometric Functions of Kummer _1F_1 (a; b; x) and Tricomi  ψ(a, b; x)
		2.21. The Gauss Hypergeometric Function _2F_1(a,b; c; x)
		2.22 The Generalized Hypergeometric Function _pF_q((a_p); (b_q); x) and Hypergeometric  Functions of Two Variables
		2.23 The MacRobert E-Function E(p; a_r:q; b_s:x)
		2.24 The Meijer G-Function G^{mn}_{pq}(x | (a_p)(b_q))
		2.25 The Fox H-Function H^{mn}_{pq}[x | [a_p, A_p][b_q, B_q]]
		2.26 The Theta Functions θ_j (x,q)
		2.27 The Mathieu Functions
		2.28 The Functions ν(x), ν(x,ρ), µ(x,λ), µ(x,m,n), λ(x,a)
	Chapter 3. Definite Integrals of Piecewise-Continuous Functions
		3.1 Introduction
		3.2 Piecewise-Constant Functions
		3.3 Some Piecewise-Continuous Functions
	Chapter 4. Multiple Integrals
		4.1 Introduction
		4.2 Doubie lntegrais
		4.3 Multiple Integrals
	Chapter 5. Finite Sums
		5.1 The Numbers and Polynomials of Bernoulli B_n, B_n(x) and Euler E_n, E_n(x)
		5.2 The Legendre Functions P^μ_ν(x) and Q^μ_ν(x)
		5.3 The Generalized Hypergeometric Function _pF_q((a_p); (b_q); x) and the Meijer G-Function
	Chapter 6. Series
		6.1 Introduction
		6.2 The Generalized Zeta Function ζ(s,v)
		6.3 The numbers and polynomials of Bernoulli B_n, B_n(x) and Euler E_n, E_n(x)
		6.4 The Functions of Struve H_ν(x), Weber E_ν(x) and Anger J_ν(x)
		6.5 The Legendre Functions P^μ_ν(x) and Q^μ_ν(x)
		6.6 The Kummer Confluent Hypergeometric Function _1F_1 (a; b; x)
		6.7 The Gauss Hypergeometric Function _2F_1 (a, b; c; x)
		6.8 The Generalized Hypergeometric Function _pF_q((a_p); (b_q); x)
		6.9 Various Hypergeometric Functions
		6.10 The MacRobert E-Function E(p; a_r:q; b_s:x)
		6.11 The Meijer G-Function G^{mn}_{pq}(x | (a_p)(b_q))
		6.12 Various Series
	Chapter 7. The Hypergeometric Functions: Properties, Representations, Particular Values
		7.1 Introduction
		7.2 The Main Properties of the Hypergeometric Functions
		7.3 The Functions _1F_0(a; z) and _2F_1(a,b; c; z)
		7.4 The Function _3F_2(a_1,a_2,a_3; b_1,b_2; z)
		7.5 The Function _4F_3(a_1,a_2,a_3,a_4; b_1,b_2,b_3; z)
		7.6 The Function _5F_4(a_1,…,a_5; b_1,…,b_4; z)
		7.7 The Function _6F_5(a_1,…,a_6; b_1,…,b_5; z)
		7.8 The Function _7F_6(a_1,…,a_7; b_1,…,b_6; z)
		7.9 The Function _8F_7(a_1,…,a_8; b_1,…,b_7; z) and _9F_8(a_1,…,a_9; b_1,…,b_8; z)
		7.10 The Function _{q+1}F_q((a_{q+1}); (b_q); z)
		7.11 The Functions of Kummer _1F_1(a;b;z) and Tricomi Ψ(a,b;z)
		7.12 The Functions _2F_2(a_1,a_2;b_1,b_2;z) and _qF_q((a_q);(b_q);z)
		7.13 The Function _0F_1(b; z)
		7.14 The Function _1F_2(a_1; b_1,b_2; z)
		7.15 The Function _2F_3(a_1,a_2; b_1,b_2,b_3; z)
		7.16 Functions of the Form _0F_q((b_q); z), q=2, 3
		7.17 Functions of the form _pF_0 (-n, (a_{p-1}); z), P= 2, 3
		7.18 Various Hypergeometric Functions
	Chapter 8. The Meijer G-Function and the Fox H-Function
		8.1 Introduction
		8.2 The Meijer G-Function G^{mn}_{pq}(z | (a_p)(b_q))
		8.3 The Fox H-Function H^{mn}_{pq}[x | [a_p, A_p][b_q, B_q]]
		8.4 Table of Mellin Transforms and Representations of Elementary and Special Functions in Terms of the Meijer G-Function and the Fox H-Function
			8.4.1 Formulae of general form
			8.4.2 Power functions and algebraic functions
			8.4.3 The exponential function
			8.4.4 The hyperbolic functions
			8.4.5 The trigonometric functions
			8.4.6 The logarithmic function
			8.4.7 The inverse trigonometric functions
			8.4.8 The inverse hyperbolic functions
			8.4.9 The polylogarithm Li_n(x)
			8.4.10. The function Φ(χ, s, v)
			8.4.11 The integral exponential function Ei(x)
			8.4.12 The integral sines Si(x), si(x) and cosine ci(x)
			8.4.13 The integral hyperbolic sine shi(x) and cosine chi(x)
			8.4.14 The error functions erf(x), erfc(x) and erfi(x)
			8.4.15 The Fresnel integrals S(x) and C(x)
			8.4.16 The incomplete gamma-functions γ(v,x) and Γ(v,x)
			8.4.17 The generalized Fresnel integrals S(x, v) and C(x, v)
			8.4.18 The parabolic cylinder function D_ν(x)
			8.4.19 The Bessel function J_ν(x)
			8.4.20 The Neumann function Y_ν(x)
			8.4.21 The Hankel functions H^{(1)}_ν(x) and H^{(2)}_ν(x)
			8.4.22 The modified Bessel function I_ν(x)
			8.4.23 The MacDonald function K_ν(x)
			8.4.24 The integral Bessel functions Ji_ν(x), Yi_ν(x) and Ki_ν(x)
			8.4.25 The Struve functions H_ν(x) and L_ν(x)
			8.4.26 The functions of Weber E_ν(x), E^μ_ν(x) and Anger J_ν(x), J^μ_ν(x)
			8.4.27 The Lommel functions s_μ, ν(x) and S_{μ,v}(x)
			8.4.28 The Kelvin functions ber_ν(x), bei_ν(x), ker_ν(x) and kei_ν(x)
			8.4.29 The Airy functions Ai(x) and Bi(x)
			8.4.30 The Legendre polynomials P_n(x)
			8.4.31 The Chebyshev polynomials of the first kind T_n(x)
			8.4.32 The Chebyshev polynomials of the second kind U_n(x)
			8.4.33 The Laguerre polynomials L^λ_n(x) and L_n(x)
			8.4.34 The Hermite polynomials H_n(x)
			8.4.35 The Gegenbauer polynomicals C^λ_n(x)
			8.4.36 The Jacobi polynomials P^{ρ,σ}_n(x)
			8.4.37 The Laguerre function L_ν(x)
			8.4.38 The Bateman function k_ν(x)
			8.4.39 The Lommel function U_ν(x,z)
			8.4.40 The complete elliptic integrals K(x), E(x), D(x)
			8.4.41 The Legendre functions of the first kind P^μ_ν(x) and P_ν(x)
			8.4.42 The Legendre functions of the second kind Q^μ_ν(x) and Q_ν(x)
			8.4.43 The Whittaker function M_{ρ,σ}(x)
			8.4.44 The Whittaker function W_{ρ,σ}(x)
			8.4.45 The confluent hypergeometric function of Kummer _1F_1(a;b;x)
			8.4.46 The confluent hypergeometric function of Tricomi Ψ(a,b;x)
			8.4.47 The function _0F_1(b; x)
			8.4.48 The function _1F_2(a; b_1, b_2; x)
			8.4.49.The Gauss hypergeometric function_2F_1 (a, b; c; x)
			8.4.50 The function _3F_2(a_1,a_2,a_3; b_1,b_2; x)
			8.4.51 Various functions of hypergeometric type
			8.4.52 Index of particular cases of the Meijer G-function and the Fox H-function
	Appendix I. Some Properties of Integrals, Series, Products and Operations with them
		I.1 Introduction
		I.2 Convergence of Integrals and Operations with them
		I.3 Convergence of Series and Products and Operations with them
	Appendix II. Special Functions and their Properties
		II.1 The Binomial Coefficients (a b)
		II.2 The Pochhammer Symbol (a)_k
		II.3 The Gamma Function Γ(z)
		II.4 The Psi-Function ψ(z)
		II.5 The Polylogarithm Li_ν(z)
		II.6 The Generalized Fresnel Integrals S(z,v) and C(z,v)
		II.7 The Generalized Zeta-Function ζ(z,v)
		II.8 The Bernoulli Polynomials B_n(z) and the Bernoulli Numbers B_n
		II.9 The Euler Polynomials E_n(z) and the Euler Numbers E_n
		II.10 The Struve Functions H_ν(z) and L_ν(z)
		II.11 The Functions of Weber E_ν(z), E^μ_ν(z) and Anger J_ν(z), J^μ_ν(z)
		II.12 The Lommel Functions s_{μ,ν}(z) and S_{μ,ν}(z)
		II.13 The Kelvin functions ber_ν(z), bei_ν(z), ker_ν(z) and kei_ν(z)
		II.14 The Airy functions Ai(z), Bi(z)
		II.15 The integral Bessel functions Ji_ν(z), Yi_ν(z), Ki_ν(z)
		II.16 The Incomplete Elliptic Integrals F(φ,k), E(φ,k), D(φ,k), Π(φ,ν,k), Δ_0(φ,β,k) and the Complete Elliptic Integrals K(k), E(k), D(k)
		II.17 The Bateman Function k_ν(z)
		II.18 The Legendre Functions P_ν(z), P^μ_ν(z), Q_ν(z), Q^μ_ν(z)
		II.19 The MacROBERT E-Function E(p; a_r:q ; b_s:z)
		II.20 The Jacobi Elliptic Functions cn u, dn u, sn u
		II.21 The Weierstrass Elliptic Functions ????(u), ζ(u), σ(u)
		II.22 The Theta-Function θ_j z,q),  j=0,1,2,3,4
		II.23 The Mathieu Functions
		II.24 The Polynomials of Neumann O_n(z) and Schläfli S_n(z)
		II.25 The Functions ν(z), ν(z,ρ), μ(z,λ), μ(z,λ,ρ)
	Bibliography
		[21]
		[46]
	Index of notations for functions and constants
	Index of mathematical symbols
Integrals and Series Vol.4 - Direct Laplace Transforms(1992)
	Cover
	Half Title
	Title Page
	Copyright Page
	Table of Contents
	Preface
	Chapter 1. Formulas of General Form
		1.1 Transforms Containing Arbitrary Functions
			1.1.1. Basic formulas
			1.1.2. f(A(x)) and algebraic functions
			1.1.3. f(ip{x)) and non-algebraic functions
			1.1.4. Derivatives of f ( x )
			1.1.5. Integrals containing f(x)
	Chapter 2. Elementary Functions
		2.1 The Power and Algebraic Functions
			2.1.1. Functions of the form xv,θ(±x=Fa)xv, [xt
			2.1.2. Functions of the form (x+z)", (a-x):
			2.1.3. Functions of the form x^{x zY , x^ {a - xY^
			2.1.4. Functions of the form x^\x^/^ + z)'', x^{a — x^^^Y± for / ^ A:
			2.1.5. Functions containing y/ x -\-z
			2.1.6. Functions containing ± z^/^ ior I ^ k
			2.1.7. Functions of [x]
		2.2 The Exponential Function
			2.2.1. exp ( -a.xflk) and the power function
			2.2.2. exp ( -ax-lfk) and the power function
			2.2.3. exp ( -ax±lfk) and algebraic functions
			2.2.4. Functions of the form f (x, e-ax,e-bx,e-cx, ... )
			2.2.5. Functions containing exp ( -av x2 .± b2)
			2.2.6. Functions containing exp (f(x))
			2.2.7. Functions of [x]
		2.3 Hyperbolic Functions
			2.3.1. , Hyperbolic functions of ax
			2.3.2. Hyperbolic functions of ax and the power function
			2.3.3. Hyperbolic functions of ax l/-for l^ k and algebraic functions
			2.2.4. Functions of the formf (x, e-ax,e-bx,e-cx, ... )
			2.3.5. ±b +x and algebraic functions
			2.3.6. Hyperbolic functions of ax^ the power and exponential functions
			2.3.7. Hyperbolic functions of ax~ for the power and algebraic functions
			2.3.8. Hyperbolic functions of
			2.3.9. Hyperbolic functions oi fie ) and the exponential function
			2.3.10. Functions containing the exponential function of hyperbolic functions
		2.4 Trigonometric Functions
			2.4.1. Trigonometric functions of ax
			2.4.2. Trigonometric functions of ax and the power function Uk
			2.4.3. Trigonometric functions of ax algebraic functions for l^ k and
			2.4.4. Trigonometric functions of ax function and the power
			2.4.5. Trigonometric functions functions of J x ^+ x z and algebraic
			2.4.6. Trigonometric functions of a\±b^-^x^ functions and algebraic
			2.4.7. Trigonometric functions of ax, the power and exponential function
			2.4.8. Trigonometric functions of ax~ for l^k, the power and exponential functions
			2.4.9. Trigonometric functions of [x]
			2.4.10. Trigonometric functions of f (e-x) and the exponential function
			2.4.11. Trigonometric and hyperbolic functions
		2.5 The Logarithmic Function
			2.5.1. XvL^iax) and algebraic functions
			2.5.2. ln”t o “^^^+5) and algebraic functions
			2.5.3. Functions of the form \ni\ x ^ ^ ^ ^->ra x ^ ^ ^ and algebraic functions
			2.5.4. ln nx, the power and exponential functions
			2.5.5. The logarithmic function of f  and the exponential function
			3.17.3. H {ax ), L {ax ' ) and hyperbolic functions
			3.17.4. ^ )» \.^{ax^ ) and trigonometric functions
			3.17.5. H (nx) and the Bessel function J {ax)
			3.17.6. ^y,(^x ) - H^(nx ) and the power function
			3.17.7. - H^ (. ax l/L), bei (ax )
			3.19.6. ker^" Xax l/k) , kei^'(' izx Uk) and the power function
			3.19.7. ker^(ae~^^), kei^(ae~^^) and the exponential function
			3.19.8. ker^to^^S, kei^(ax*^^) and hyperbolic functions
			3.19.9. ker^(ax*^S, kei^(ax*^S and trigonometric functions
			3.19.10. The Kelvin functions and the logarithmic function
		3.20 The Airy Functions Ai(z) and Bi(z)
			3.20.1. A ito ), E\(ax ) and the power function
			3.20.2. Ai(ax ), Bi), E(/(x)), K(f(x)) and hyperbolic functions
			3.31.5. D(/(x)), E(f(x)), K(f(x)) and trigonometric functions
		3.32 The Legendre Functions of The First Kind P^μ_ν(z)
			3.32.1. P^(f(x)) and algebraic functions
			3.32.2. Pjj(/;(ox 2.) and hyperbolic functions
			3.35.5. and trigonometric functions
			3.35.6. jFj(a;^;o)x) and various functions
			3.35.7. Products of jFj(fl;5;(i)x)
		3.36 The Tricomi Confluent Hypergeometric Function Ψ(a,b;z)
			3.36.1. T*(n,5;tox± l/k) and the power function
			3.36.2. 'F(n,6,/(x)) and the exponential function
			3.36.3. T'(n,5;/(e~^)) and the exponential function
			3.36.4. T^(a,5,(i)x“^) and hyperbolic functions
			3.36.5. functions
			3.36.6. and trigonometric functions
			3.36.7. W(ajb;(i)x^^) the exponential and trigonometric functions
			3.36.8. Products and the power function
			3.36.9. Products F (a;^;-a)e~^)'F(a,^;(oe“^)
			3.36.10. Products of ^(a,A;ti)x k), the power and exponential functions
			3.36.11. Products of T‘(a,^;a)e zfcX) and the exponential function
		3.37 The Gauss Hypergeometric Function _2F_1(a,b;c;z)
			3.37.1. ^^ {a,b;c;-(ox± k) and the power function
			3.37.2. ^F^(a,b;c;f(x)) and algebraic functions
			3.37.3. ^F^(a,b;c;f(e~^)) and the exponential function
		3.38 The Generalized Hypergeometric Function _mF_n((a_m);(b_n);z)
			3.38.1. mF n((ta n);{nb );(ox k) and the power function
			3.38.2. exponential function
			3.38.3. ^F^((a^)±[x];(5^)±[x];o)) and various functions
		3.39 The MacROBERT E-Function E(μ ; a_r:ν ; b_s:z)
		3.40 The Meijer G-Function G^{mn}_{uv}(z| (a_u)(b_v))
			3.40.1. G-function and the power function
			3.40.2. G-function and the exponential function
			3.40.3. G-function with [x] in parameters
			3.40.4. Products of G-functions
		3.41 Theta-Functions θ_j(z,q), \hat{θ}_j(z,q)
			3.41.1. e.(aiix,g), 0^.(v,e”^)
			3.41.2. 0^.(v,ax)
		3.42 The Functions ν(z), ν(z,Q), μ(z,λ), μ(z,λ,Q), λ(z,Q)
			3.42.1. v(ax^^^),v(e”^ ) , the power and exponential functions
			3.42.2. v(e”^,Q) and the power function
			3.42.3. and the power function
			3.42.4. and the power function
			3.42.5. Xiax *,q) and the power function
		3.43 The Confluent Hypergeometric Functions of Two Variables
			3.43.1. Confluent hypergeometric functions and the power function
	Appendix. Elements of The Theory of The Laplace Transformation
		1. The Laplace transform and its basic properties
		2. The Application of the Laplace Transformation to the Solution of Differential and Integral Equations
		3. Some Comments and References
	Bibliography
		[15]
		[32]
		[50]
		[69]
		[87]
	List of Notations of Functions and Constants
	List of Mathematical Symbols
Integrals and Series Vol.5 - Inverse Laplace Transforms(1992)
	Contents
	Preface
	Chapter 1. General Formulas
		1.1 Transforms Containing Arbitrary Functions
	Chapter 2. Elementary Functions
		2.1 The Power and Algebraic Functions
		2.2 The Exponential Function
		2.3 Hyperbolic Functions
		2.4 Trigonometric Functions
		2.5 The Logarithmic Function
		2.6 Inverse Trigonometric Functions
		2.7 Inverse Hyperbolic Functions
	Chapter 3. Special Functions
		3.1 The Gamma Function Γ(z) and the Psi Function ψ(z)
		3.2 The Riemann Zeta Function ζ(z), The Functions ζ(z,v) and Φ(z,s,v)
		3.3 The Polylogarithm Li_n(z)
		3.4 The Exponential Integral Ei(z)
		3.5 The Sine Integrals si(z), Si(z) and the Cosine Integral ci(z)
		3.6 The Hyperbolic Sine shi(z) and Cosine Integrals chi(z)
		3.7 The Error Functions erf(z), erfc(z) and erfi(z)
		3.8 The Sine and Cosine Fresnel Integrals S(z) and C(z)
		3.9 The Generalized Fresnel Integrals S(z,v) and C(z,v)
		3.10 The Incomplete Gamma Functions γ(v,z) and Γ(v,z)
		3.11 The Parabolic-Cylinder Function D_ν(z)
		3.12 The Bessel Function J_ν(z)
		3.13 The Neumann Function Y_ν(z)
		3.14 The Hankel Functions H^{(1)}_ν(z), H^{(2)}_ν(z)
		3.15 The Modified Bessel Function I_ν(z)
		3.16 The MacDONALD Function K_ν(z)
		3.17 The Struve Functions H_ν(z) and L_ν(z)
		3.18 The Anger Function J_ν(z) and The Weber Function E_ν(z)
		3.19 The Kelvin Functions ber_ν(z), bei_ν(z), ker_ν(z), kei_ν(z)
		3.20 The Legendre Polynomials P_n(z)
		3.21 The Chebyshev Polynomials T_n(z) and U_n(z)
		3.22 The Laguerre Polynomials L^ν_n(z)
		3.23 The Hermite Polynomials H_n(z)
		3.24 The Gegenbauer Polynomials C^ν_n(z)
		3.25 The Jacobi Polynomials P^{(μ,ν)}_n(z)
		3.26 The Bernoulli B_n(z), Euler E_n(z) and Neumann O_n(z) Polynomials
		3.27 The Bateman Function k_ν(z)
		3.28 The Laguerre Function L_ν(z)
		3.29 The Complete Elliptic Integrals D(k), E(k) and K(k)
		3.30 The Legendre Functions of The First Kind P^μ_ν(z)
		3.31 The Legendre Functions of The Second Kind Q^μ_ν(z)
		3.32 The Lommel Functions s_{μ,ν}(z) and S_{μ,ν}(z)
		3.33 The Kummer Confluent Hypergeometric Function _1F_1(a;b;z)
		3.34 The Tricomi Confluent Hypergeometric Function Ψ(a,b;z)
		3.35 The Gauss Hypergeometric Function _2F_1(a,b;c;z)
		3.36 The Generalized Hypergeometric Function _mF_n((a_m);(b_n);z)
		3.37 The MacROBERT E-Function E(μ ; a_r:ν ; b_s:z)
		3.38 The Meijer G-Function G^{m,n}_{u,v}(z| (a_u)(b_v))
		3.39 The Functions ν(z), ν(z,a), μ(z,a), μ(z,a,b), λ(z,a)
		3.40 The Hypergeometric Functions of Two Variables(The Appell Functions)
	Chapter 4. Integral Transforms and their Factorization
		4.1 Introduction
			4.1.1 Definition and classification of integral transforms
			4.1.2 Definition of factorization
			4.1.3 The Mellin transform and factorization
			4.1.4 Correspondences between kernels and their Mellin transforms
			4.1.5 Some principal integral transforms
			4.1.6 Table of factorizations of some principal integral transforms
		4.2 Table of Factorizations for Integral Transforms of the Mellin-Convolution Type
			4.2.1 Algebraic functions and powers with arbitrary exponent
			4.2.2 Trigonometric functions
			4.2.3 The logarithmic function
			4.2.4 Hyperbolic and inverse hyperbolic functions
			4.2.5 Inverse trigonometric functions
			4.2.6 Special cases of Whittaker functions
			4.2.7 Bessel functions
			4.2.8 Orthogonal polynomials
			4.2.9 The Legendre functions
			4.2.10 Hypergeometric functions
		4.3 Table of Integral Transforms and their Factorizations
			4.3.1 General formulas
			4.3.2 The power and algebraic functions
			4.3.3 The exponential function
			4.3.4 Hyperbolic functions
			4.3.5 Trigonometric functions
			4.3.6 The logarithmic function
			4.3.7 The inverse trigonometric functions
			4.3.8 The gamma function Γ(z)
			4.3.9 The generalized Riemann zeta function ζ(z,v)
			4.3.10 The exponential integral Ei(z)
			4.3.11 The logarithmic integral li(z)
			4.3.12 The sine integrals si(z), Si(z) and the cosine integral ci(z)
			4.3.13 The error function erf(z)
			4.3.14 The Fresnel integrals S(z), C(z)
			4.3.15 The generalized Fresnel integrals S(z,v), C(z,v)
			4.3.16 The incomplete gamma functions γ(v,z), Γ(v,z)
			4.3.17 The parabolic-cylinder function D_ν(z)
			4.3.18 The Bessel function J_ν(z)
			4.3.19 The Neumann function Y_ν(z)
			4.3.20 The Hankel functions  H^{(1)}_ν(z), H^{(2)}_ν(z)
			4.3.21 The modified Bessel function I_ν(z)
			4.3.22 The MacDonald function K_ν(z)
			4.3.23 The Struve function H_ν(z)
			4.3.24 The Kelvin functions
			4.3.25 The Airy function Ai(z)
			4.3.26 The Legendre polynomials P_n(z)
			4.3.27 The Chebyshev polynomials of the first kind T_n(z)
			4.3.28 The Chebyshev polynomials of the second kind U_n(z)
			4.3.29 The Laguerre polynomials L^ν_n(z)
			4.3.30 The Hermite polynomials H_n(z)
			4.3.31 The Gegenbauer polynomials C^ν_n(z)
			4.3.32. The Jacobi polynomials P^{(μ,ν)}_n(z)
			4.3.33 The complete elliptic integral of the first kind K(z)
			4.3.34 The Legendre function of the first kind P_ν(z)
			4.3.35 The associated Legendre function of the first kind P^μ_ν(z)
			4.3.36 The Legendre function of the second kind Q_ν(z)
			4.3.37 The assosiated Legendre function of the second kind Q^μ_ν(z)
			4.3.38. The Lommel function s_{μ,ν}(z)
			4.3.39 The Whittaker confluent hypergeometric function M_{μ,ν}(z)
			4.3.40 The Whittaker confluent hypergeometric function W_{μ,ν}(z)
			4.3.41 The Kummer confluent hypergeometric function _1F_1(a;c;z)
			4.3.42 The Tricomi confluent hypergeometric function Ψ(a,c;z)
			4.3.43 The Gauss hypergeometric function _2F_1(a,b;c;z)
			4.3.44 The generalized hypergeometric function _pF_q((a_p);(b_q);z)
			4.3.45 The Meijer G-function
			4.3.46 The elliptic theta functions θ_j(z,q)
			4.3.47 The functions ν(x), E_Q(x,μ)
			4.3.48 The hypergeometric functions of the two variables
	Bibliography
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	Index of Notations for Functions and Constants
	Index of Mathematical Symbols