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 |
THE GAMMA AND BETA FUNCTIONS | 8 |
Eulers integral for rz | 15 |
Copyright | |
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Common terms and phrases
a₁ absolutely convergent analytic asymptotic expansion b₁ b₂ basic table Bateman Bessel functions Bessel polynomials Chapter coefficients conclude constant defined derive differential equation differential recurrence relation elliptic function exists exp(−x² exp(2xt F₁ F₁(a 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 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 set of polynomials Sheffer A-type zero Show simple set sn(u Sn(x solution Theorem 48 theta functions Watson's lemma write yields ακ Σ Σ ΣΣ