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Special Functions
editA Companion to Wang and Kuo's Introduction
edit- 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