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Chapter 8. Special Functions
Table of Contents
Number Series
Bernoulli Numbers
Tangent Numbers
Prime Numbers
Fibonacci Numbers
Gamma Functions
Gamma
Log Gamma
Digamma
Trigamma
Polygamma
Ratios of Gamma Functions
Incomplete Gamma Functions
Incomplete Gamma Function Inverses
Derivative of the Incomplete Gamma Function
Factorials and Binomial Coefficients
Factorial
Double Factorial
Rising Factorial
Falling Factorial
Binomial Coefficients
Beta Functions
Beta
Incomplete Beta Functions
The Incomplete Beta Function Inverses
Derivative of the Incomplete Beta Function
Error Functions
Error Function erf and complement erfc
Error Function Inverses
Polynomials
Legendre (and Associated) Polynomials
Legendre-Stieltjes Polynomials
Laguerre (and Associated) Polynomials
Hermite Polynomials
Chebyshev Polynomials
Spherical Harmonics
Cardinal B-splines
Gegenbauer Polynomials
Jacobi Polynomials
Bessel Functions
Bessel Function Overview
Bessel Functions of the First and Second Kinds
Finding Zeros of Bessel Functions of the First and Second Kinds
Modified Bessel Functions of the First and Second Kinds
Spherical Bessel Functions of the First and Second Kinds
Derivatives of the Bessel Functions
Hankel Functions
Cyclic Hankel Functions
Spherical Hankel Functions
Airy Functions
Airy Ai Function
Airy Bi Function
Airy Ai' Function
Airy Bi' Function
Finding Zeros of Airy Functions
Elliptic Integrals
Elliptic Integral Overview
Elliptic Integrals - Carlson Form
Elliptic Integrals of the First Kind - Legendre Form
Elliptic Integrals of the Second Kind - Legendre Form
Elliptic Integrals of the Third Kind - Legendre Form
Elliptic Integral D - Legendre Form
Jacobi Zeta Function
Heuman Lambda Function
Jacobi Elliptic Functions
Overview of the Jacobi Elliptic Functions
Jacobi Elliptic SN, CN and DN
Jacobi Elliptic Function cd
Jacobi Elliptic Function cn
Jacobi Elliptic Function cs
Jacobi Elliptic Function dc
Jacobi Elliptic Function dn
Jacobi Elliptic Function ds
Jacobi Elliptic Function nc
Jacobi Elliptic Function nd
Jacobi Elliptic Function ns
Jacobi Elliptic Function sc
Jacobi Elliptic Function sd
Jacobi Elliptic Function sn
Jacobi Theta Functions
Overview of the Jacobi Theta Functions
Jacobi Theta Function θ
1
Jacobi Theta Function θ
2
Jacobi Theta Function θ
3
Jacobi Theta Function θ
4
Lambert
W
function
Zeta Functions
Riemann Zeta Function
Exponential Integrals
Exponential Integral En
Exponential Integral Ei
Hypergeometric Functions
Hypergeometric
1
F
0
Hypergeometric
0
F
1
Hypergeometric
2
F
0
Hypergeometric
1
F
1
Hypergeometric
p
F
q
Hypergeometric References
Basic Functions
sin_pi
cos_pi
log1p
expm1
cbrt
sqrt1pm1
powm1
hypot
Compile Time Power of a Runtime Base
Reciprocal square root
logaddexp and logsumexp
Sinus Cardinal and Hyperbolic Sinus Cardinal Functions
Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview
sinc_pi
sinhc_pi
Inverse Hyperbolic Functions
Inverse Hyperbolic Functions Overview
acosh
asinh
atanh
Owen's T function
Daubechies Wavelets and Scaling Functions
Constexpr CMath
