Innovative Integrals and Their Applications II (STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health)

Preface
	References
Contents
1 An Overview of the Methods
	1 Special Functions
		1.1 The Gamma Function and the Factorial
		1.2 The Error Function and the Inverse Error Function
		1.3 Bessel Functions and Modified Bessel Functions
		1.4 The Rectangle Function and the Heaviside Step Function
		1.5 The Signum Function
		1.6 The Owen T-Function
		1.7 The Exponential Integral and the Logarithmic Integral
		1.8 The Cosine Integral and the Sine Integral
		1.9 Hypergeometric Functions
		1.10 Elliptic Integrals and Jacobi Elliptic Functions
		1.11 The Polygamma Function and the Harmonic Number
		1.12 The Polylogarithm
		1.13 The Riemann Zeta Function and the Hurwitz Zeta Function
		1.14 The Lerch Transcendent
		1.15 The Incomplete Beta Function
		1.16 Struve Functions and Modified Struve Functions
		1.17 The Lambert W-Function
		1.18 Fresnel Integrals
		1.19 The Laguerre Polynomial
		1.20 The Meijer G-Function
		1.21 Dawson\'s Integral
	2 Fundamental Constants
		2.1 The Euler-Mascheroni Constant
		2.2 Catalan\'s Constant
		2.3 The Stieltjes Constants
	3 The Generalized Method of Exhaustion
		3.1 An Infinite Product
		3.2 An Alternative Form
	4 Multivariate Substitution
		4.1 Some Examples
	5 Permutation Symmetry
	6 Interchanging the Order of Integration
	7 Is It New?
	8 A Word on Innovation
	9 Exercises
	References
2 Warm-Up: Interchanging the Order of Integration
	1 Preliminary
		1.1 Theoretical Considerations
		1.2 Examples
	2 Triple Integrals
	3 More Double Integrals
	4 Integrals with Finite Limits of Integration
	5 Exercises
3 Permutation Symmetry
	1 Preliminary
	2 Results Involving the Exponential Integral Function
	3 Results Involving the Polylogarithm
	4 Results Involving Bessel Functions
	5 Miscellaneous Results
	6 Integrals with Finite Limits of Integration
	7 Exercises
	References
4 Identities Involving Laplace Transforms and Fourier Transforms
	1 Introduction
		1.1 The Laplace Transform
		1.2 The Fourier Transform
	2 The Use of Laplace Transform Pairs
	3 Laplace Transform Pairs
	4 Fourier Transform Pairs
		4.1 Previous Results, Reinterpreted
		4.2 New Results
		4.3 Related Fourier Transform and Laplace Transform Pairs
	5 The Use of Fourier Transform Pairs
	6 Exercises
	References
5 A Potpourri of Methods and Results
	1 Preliminary Results
	2 Identities Involving Bessel Functions and Struve Functions
	3 Identities Involving the Riemann Zeta Function and the Hurwitz Zeta Function
	4 Identities Involving the Owen T-Function
	5 Results Involving the Polygamma Function and the Harmonic Number
	6 Identities Involving the Polylogarithm
	7 Postliminary Results
	8 Exercises
6 Applications in the Sciences, Technology, and Engineering
	1 Non-Gaussian Distributions
		1.1 An Improved Proof
		1.2 Finite Limits of Integration
	2 Weighted Gaussian Distributions
		2.1 An Improved Proof
		2.2 Finite Limits of Integration
	3 Weighted Non-Gaussian Distributions
	4 Benchmarks for Cubature Formulas
		4.1 An Old Result
		4.2 New Results
		4.3 Finite Limits of Integration
	5 The Reciprocal of a Complex Number
		5.1 The Sommerfeld Integral
		5.2 A Family of Expansions
		5.3 Other Applications
	6 Exercises
	References
Bibliography
Index