Special Functions for Scientists and Engineers

a₁ ax Jo(bx Bessel's equation Bessel's modified equation beta function binomial theorem change of variable Chebyshev polynomials confluent hypergeometric function convergent day dx2 defined definition 4.26 differential equation dx2 dx equation 4.6 exp 2tx exp i{x expanded finite FUNCTIONS Theorem gamma function Gegenbauer polynomials gives Hence HERMITE POLYNOMIALS Hn(x hypergeometric function In(x independent solutions indicial equation integral J_n(x Jacobi polynomials Jn(ix Jn(x JnYn Jo(x Kn(x L'Hôpital's rule Laguerre polynomials Legendre functions Legendre polynomials Legendre's equation Ln(x n²)y non-integral obtain P₁(x polynomial of degree power series PROOF recurrence relation required result result of theorem right-hand side s₁ satisfies second kind series solutions Show sin² sinx solution of equation solutions of Bessel's spherical Bessel functions theorem 4.8 Tn(x Un(x values xn+1 y₁(x Yn(x zero ηπ νπ π π πχ χη