Special Functions"Based upon the lectures on special functions which ... (the author has) been giving at the University of Michigan since 1946.". |
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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 |
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a₁ absolutely convergent analytic asymptotic expansion b₁ b₂ Bateman Bessel functions Bessel polynomials Chapter coefficients conclude constant contiguous function relations defined denominator parameter derive differential equation differential recurrence relation elementary elliptic function exp(−x² exp(2xt F₁ factor finite follows formula Gegenbauer polynomials Hence Hermite polynomials Hn(x hypergeometric function hypergeometric series infinite product integral Jacobi polynomials Laguerre polynomials Laplace transform left member Legendre polynomials Lim 4u negative integer nomials non-negative integer notation obtain on(x orthogonal P₂(x Pn(x poles poly polynomial sets power series preceding section Proof properties pure recurrence relation Re(b Re(c Re(z region replace right member Rodrigues formula set of polynomials Sheffer A-type zero Show simple set sn(u Sn(x solution term Theorem theta functions variable W₁ Watson's lemma write yields Σ Σ ΣΣ