Special Functions |
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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a₁ absolutely convergent Amer analytic asymptotic expansion b₁ basic table Bateman Bessel functions Bessel polynomials Boas and Buck Brafman c)nn Chapter coefficients conclude constant defined degree precisely derive differential equation differential recurrence relation elliptic function exp(2xt F₁ F₁(a factor finite follows formula Gegenbauer polynomials Hence Hermite polynomials Hn(x hypergeometric function hypergeometric series integral Jacobi polynomials Laguerre polynomials left member Legendre polynomials Lemma negative integer nomials non-negative integer notation obtain on(x orthogonal polynomials orthogonal set P₂(x parameters Pn(x poles poly polynomial of degree polynomial sets preceding section Proof properties pure recurrence relation right member Rodrigues formula set of polynomials Sheffer A-type zero Show simple set Sister Celine's sn(u solution T₁(x Theorem Theorem 48 Theorem 57 theta functions yields Σ Σ ΣΣ