Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions |
Contents
The Gamma Function and the Beta Function | 1 |
Table of Formulas | 49 |
Infinite Product Expression of π2 | 58 |
Copyright | |
26 other sections not shown
Common terms and phrases
A₁ apply Eq arbitrary constants becomes infinite Bessel functions Beta function C₁ and C₂ coefficients convergent coordinates cylinder determine differential equation equal established in Prob evaluated factor find that Eq finite follows Gamma function given by Eq identically indeterminate form infinite series integral in Eq integrand interval iterated integral J₁(x Jo(x Laplace's equation left side Legendre duplication formula Legendre polynomials Legendre's equation Leibniz's rule loge Maclaurin series multiplied namely negative obtained odd function P₁(x P₂(x particular solution Pn(x Po(x polynomial of degree positive integer powers of h present problem R₁ R₂ REMARK requires right in Eq right side satisfies Laplace's equation series in Eq side of Eq sinh solution of Eq summation surface Table V-1 temperature distribution term termwise vanishes x²y z-axis дх