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 | |
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A-type already analytic apply argument arrive b₁ becomes Bessel functions c)nn called Chapter coefficients conclude condition Consider constant contiguous function convergent defined definition denominator derive desired differential equation easily elementary evaluate example EXERCISES exists F₁ factor Figure finite follows formula function Hence Hermite identity independent infinite integral involving later leads Legendre polynomials Lemma method negative integer non-negative notation Note obtain once operator orthogonal parameters periods Pn(x poles polynomials positive preceding Proof properties prove pure recurrence relation region replace result satisfied Section Sheffer Show shown simple solution term Theorem transform valid variable Watson's write written yields zero Σ Σ ΣΣ