Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions |
Contents
The Gamma Function and the Beta Function | 1 |
Logarithmic Derivative of Tx for Positive Integers | 45 |
Infinite Product Expression of π2 | 58 |
Copyright | |
24 other sections not shown
Common terms and phrases
apply Eq arbitrary constants becomes infinite Bessel functions Beta function C₁ C₂ coefficients compute convergent coordinates cylinder determine differential equation equal established in Prob evaluated expression factor find that Eq finite follows Gamma function given by Eq identically 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 polynomial of degree positive integer powers of h present problem R₁ REMARK requires right in Eq right side satisfies Laplace's equation series in Eq side of Eq sinh solution of Eq summation surface t₁ Table V-1 temperature distribution term termwise unity vanishes x²y z-axis дх