## Special functions |

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### Contents

INFINITE PRODUCTS Page 1 Introduction | 1 |

A necessary condition for convergence | 2 |

Absolute convergence | 3 |

Copyright | |

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absolutely convergent analytic asymptotic expansion basic table Bateman Bessel functions Bessel polynomials Brafman c)nn Chapter coefficients conclude Consider constant contiguous function relations defined derive differential equation differential recurrence relation elementary elliptic function Euler evaluate exists finite follows Gegenbauer polynomials Hence Hermite polynomials Hn(x hypergeometric function hypergeometric series independent infinite product integral Jacobi polynomials Jn(z Laguerre polynomials Laplace transform left member Legendre polynomials Log(l logarithms Math negative integer nomials non-negative integer notation obtain orthogonal polynomials poles poly polynomial of degree polynomial sets polynomials pn(x positive integer power series preceding section product converges Proof properties pure recurrence relation Rainville Re(c Re(z region replace right member Rodrigues formula satisfied set of polynomials Sheffer A-type zero Show simple set Sister Celine's sn(u solution summation Theorem 48 theta functions variable Watson's lemma Weierstrass write yields