## Special functions |

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### Contents

INFINITE PRODUCTS Page 1 Introduction | 1 |

A necessary condition for convergence | 2 |

Absolute convergence | 3 |

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absolutely convergent analytic asymptotic expansion basic table Bateman Bessel functions Bessel polynomials Brafman cell Chapter cn(u coefficients conclude Consider constant contiguous function relations defined derive differential equation differential recurrence relation dn(u elementary elliptic function evaluate exists follows formula function of order Gamma function Gegenbauer polynomials Hence Hermite polynomials Hn(x hypergeometric function hypergeometric series independent infinite product integral Jacobi polynomials Laguerre polynomials left member Legendre polynomials Log(l logarithms Math negative integer nomials non-negative integer notation obtain odd function pn{x poly polynomial sets polynomials pn(x positive integer power series preceding section 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 singular points Sister Celine's sn(u solution summation Theorem 48 theta functions variable Watson's lemma Weierstrass write yields