Special Functions"Based upon the lectures on special functions which ... (the author has) been giving at the University of Michigan since 1946.". |
Contents
INFINITE PRODUCTS 1 Introduction 2 Definition of an infinite product | 1 |
A necessary condition for convergence 4 The associated series of logarithms | 2 |
Absolute convergence | 3 |
Copyright | |
100 other sections not shown
Other editions - View all
Common terms and phrases
already analytic apply argument arrive asymptotic expansion b₁ becomes called Chapter coefficients conclude condition Consider constant contiguous convergent defined definition denominator derive desired differential equation easily elementary elliptic function evaluate example EXERCISES exists F₁ factor Figure finite follows formula function Hence Hermite hypergeometric identity independent infinite integral involving known Laguerre later leads Legendre polynomials Lemma method negative integer notation Note obtain once operator orthogonal parameters periods Pn(x poles polynomials positive preceding Proof properties prove region replace result satisfied Section set of polynomials Show shown simple solution Theorem transform valid variable write written yields zero Σ Σ ΣΣ