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 Page 1 1 2 | 3 |
Copyright | |
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a₁ absolutely convergent analytic b₁ b₂ basic table Bateman's Bessel functions Bessel polynomials Brafman c)nn Celine's polynomials Chapter coefficients conclude constant contiguous function relations 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 independent infinite product integral Jacobi polynomials Laguerre polynomials left member Legendre polynomials Lemma Math negative integer nomials non-negative integer notation obtain on(x Pn(x poles poly polynomial sets preceding section Proof properties pure recurrence relation Rainville Re(a Re(b replace right member Rodrigues formula satisfied set of polynomials Sheffer A-type zero Show simple set Sister Celine's sn(u solution summation Theorem Theorem 48 theta functions W₁ write yields ακ Σ Σ ΣΣ