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Special Functions

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A Companion to Wang and Kuo's Introduction

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Series and Expansions
Bernoulli polynomials
Bernoulli number
Euler number
Euler–Maclaurin formula
Lagrange inversion theorem
Mittag-Leffler's theorem
Infinite product
Weierstrass factorization theorem
Asymptotic expansion
Watson's lemma
Frobenius method
Second Order Ordinary Differential Equations
Regular singular point
Riemann's differential equation
Hermitian adjoint
Integral transform
Cauchy–Euler equation
Gamma Function
Gamma function
Beta function
Pochhammer contour
Stirling's approximation
Riemann zeta function
Möbius function
Hypergeometric Function
Hypergeometric function
Barnes integral
Jacobi polynomials
Chebyshev polynomials
Generalized hypergeometric function
Appell series
Legendre Function
Legendre polynomials
Associated Legendre polynomials
Legendre function
Spherical harmonics
Gegenbauer polynomials
Confluent hypergeometric function
Whittaker function
Parabolic cylinder function
Hermite polynomials
Laguerre polynomials
Error function
Incomplete gamma function
Logarithmic integral function
Exponential integral
Bessel Function
Bessel function
Poisson kernel
Kelvin functions
Neumann polynomial
Airy function
Weierstrass Elliptic Function
Elliptic integral
Elliptic function
Weierstrass's elliptic functions
Theta Function
Theta function
Legendre form
Landen's transformation
Jacobi's Elliptic Function
Jacobi's elliptic functions
Lamé Function
Lamé function
Mathieu Function
Mathieu function
Hill equation
Appendix
Cubic function
Quartic function
Cylindrical coordinate system
Spherical coordinate system
Elliptic cylindrical coordinates
Parabolic cylindrical coordinates
Conical coordinates
Ellipsoidal coordinates
Prolate spheroidal coordinates
Oblate spheroidal coordinates
Parabolic coordinates
Paraboloidal coordinates
Bispherical coordinates