## Special Functions |

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### Contents

Chapter Three The Gamma Function | 7 |

Chapter Five Hypergeometric and Confluent | 15 |

Chapter Seven Spherical Harmonics | 34 |

Copyright | |

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### Common terms and phrases

Bateman Manuscript Project Bessel Functions Chapter 9 cn(u Complete Elliptic integral confluent hypergeometric function Consider the integral coth Derive differential equation dn u dn dn(u dn2 x dx dnuscu duplication formula dxz dx equation 12 equation of order Euler's constant EXERCISES h expansion fa(x Fourier Cosine transform Fourier series Fourier transform Fourier-Bessel series Gamma function Hypergeometric Equation integer or zero J-oo Jacobian Elliptic Functions Jfc2 k2 sn Laplace transform Legendre polynomials Mathematical Physics modified Bessel Normal Elliptic Integral notation obtain Orthogonality Property parameter periodic with period Pn-i Poisson Summation Formula Prove the result recurrence relations satisfies the differential series solution Show that sn sn u cd sn u sn sn(u sn2 u sn2 SPECIAL FUNCTIONS spherical harmonic theorem Theta double series Theta functions variable Verify