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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Common terms and phrases
a₁ absolutely convergent analytic asymptotic expansion b₁ b₂ basic table Bateman Bessel functions Bessel polynomials c)nn Chapter coefficients conclude constant defined derive differential equation differential recurrence relation elliptic function exists exp(2xt F₁ F₁(a factor finite follows formula Gegenbauer polynomials Hence Hermite polynomials hypergeometric function hypergeometric series infinite product integral Jacobi polynomials Laguerre polynomials left member Legendre polynomials Lim 4u negative integer nomials non-negative integer notation obtain on(x P₂(x Pn(x poles poly polynomial of degree polynomial sets power series preceding section Proof properties pure recurrence relation Re(b Re(c Re(z region replace right member Rodrigues formula satisfied set of polynomials Sheffer A-type zero Show simple set sin² sn(u solution Theorem 48 theta functions Watson's lemma write yields Σ Σ ΣΣ