An Atlas of Functions: with Equator, the Atlas Function Calculator

Front Matter....Pages i-xi
General Considerations....Pages 1-11
The Constant Function c ....Pages 13-19
The Factorial Function n !....Pages 21-27
The Zeta Numbers and Related Functions....Pages 29-38
The Bernoulli Numbers B n ....Pages 39-44
The Euler Numbers E n ....Pages 45-48
The Binomial Coefficients $\\left( {_m^v } \\right)$ ....Pages 49-56
The Linear Function bx + c and Its Reciprocal....Pages 57-65
Modifying Functions....Pages 67-74
The Heaviside u( x − a ) And Dirac δ( x − a ) Functions....Pages 75-80
The Integer Powers x n And ( bx + c ) n ....Pages 81-93
The Square-Root Function $\\sqrt {bx + c}$ and Its Reciprocal....Pages 95-102
The Noninteger Powers x v ....Pages 103-112
The Semielliptic Function $\\left( {b/a} \\right)\\sqrt {a^2 {\\kern 1pt} - x^2 }$ and Its Reciprocal....Pages 113-120
The Semihyperbolic Functions $\\left( {b/a} \\right)\\sqrt {x^2 {\\kern 1pt} \\pm a^2 }$ And Their Reciprocals....Pages 121-130
The Quadratic Function ax 2 + bx + c and Its Reciprocal....Pages 131-138
The Cubic Function x 3 + ax 2 + bx + c ....Pages 139-146
Polynomial Functions....Pages 147-158
The Pochhammer Polynomials ( x ) n ....Pages 159-174
The Bernoulli Polynomials B n ( x )....Pages 175-180
The Euler Polynomials E n ( x )....Pages 181-186
The Legendre Polynomials P n ( x )....Pages 187-196
The Chebyshev Polynomials T n ( x ) and U n ( x )....Pages 197-208
The Laguerre Polynomials L n ( x )....Pages 209-216
The Hermite Polynomials H n ( x )....Pages 217-227
The Logarithmic Function ln( x )....Pages 229-239
The Exponential Function exp(± x )....Pages 241-253
Exponentials of Powers exp(± x v )....Pages 255-267
The Hyperbolic Cosine Cosh( x ) and Sine Sinh( x ) Functions....Pages 269-279
The Hyperbolic Secant Sech( x ) and Cosecant Csch( x ) Functions....Pages 281-288
The Hyperbolic Tangent tanh( x ) and Cotangent coth( x ) Functions....Pages 289-296
The Inverse Hyperbolic Functions....Pages 297-307
The Cosine cos( x ) and Sine sin( x ) Functions....Pages 309-328
The Secant sec( x ) And cosecant csc( x ) Functions....Pages 329-338
The Tangent tan( x ) and Cotangent cot( x ) Functions....Pages 339-350
The Inverse Circular Functions....Pages 351-366
Periodic Functions....Pages 367-374
The Exponential Integrals Ei( x ) and Ein( x )....Pages 375-383
Sine and Cosine Integrals....Pages 385-394
The Fresnel Integrals C( x ) and S( x )....Pages 395-404
The Error Function erf( x ) and Its Complement erfc( x )....Pages 405-415
The $\\exp \\left( x \\right){\\mathop{\\rm erfc}\\nolimits} \\left( {\\sqrt x } \\right)$ and Related Functions....Pages 417-426
Dawson’s Integral daw( x )....Pages 427-433
The Gamma Function Γ( v )....Pages 435-448
The Digamma Function ψ( v )....Pages 449-460
The Incomplete Gamma Functions....Pages 461-470
The Parabolic Cylinder Function D v ( x )....Pages 471-484
The Kummer Function M( a , c , x )....Pages 485-496
The Tricomi Function U( a , c , x )....Pages 497-506
The Modified Bessel Functions I n ( x ) of Integer Order....Pages 507-517
The Modified Bessel Function I v ( x ) of Arbitrary Order....Pages 519-526
The Macdonald Function K v ( x )....Pages 527-536
The Bessel Functions J n ( x ) of Integer Order....Pages 537-552
The Bessel Function J v ( x ) of Arbitrary Order....Pages 553-565
The Neumann Function Y v ( x )....Pages 567-576
The Kelvin Functions....Pages 577-584
The Airy Functions Ai( x ) and Bi( x )....Pages 585-592
The Struve Function h v ( x )....Pages 593-601
The Incomplete Beta Function B( v ,μ, x )....Pages 603-609
The Legendre Functions P v ( x ) and Q v ( x )....Pages 611-626
The Gauss Hypergeometric Function F( a , b , c , x )....Pages 627-636
The Complete Elliptic Integrals K( k ) and E( k )....Pages 637-651
The Incomplete Elliptic Integrals F( k ,ϕ) AND E( k ,ϕ)....Pages 653-669
The Jacobian Elliptic Functions....Pages 671-684
The Hurwitz Function ζ( v , u )....Pages 685-695
Back Matter....Pages 697-748