## 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 asymptotic expansion basic table Bateman Bessel functions Bessel polynomials Brafman Chapter coefficients conclude constant contiguous function relations defined denominator parameter 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 Let pn(x Log(l logarithms negative integer nomials non-negative integer notation obtain poles poly polynomial of degree polynomial sets polynomials pn(x positive integer power series preceding section product converges Proof properties pure recurrence relation 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 uniformly convergent variable Watson's lemma Weierstrass write yields