Special Functions for Scientists and Engineers

a₁ an(s anxs+n aoy₁(x arbitrary constants associated Legendre Bessel's equation beta function binomial theorem change of variable Chapter Chebyshev polynomials confluent hypergeometric confluent hypergeometric function convergent defined definition 2.1 denote differential equation ds s(s dx2 dx expanded finite gamma function Gegenbauer polynomials gives the indicial gives the recurrence Hence HERMITE POLYNOMIALS Hn(x hypergeometric function In(x independent solutions indicial equation Jacobi polynomials Jn(x JnYn Jo(bx Jo(x Kn(x Laguerre polynomials left-hand side Legendre functions Legendre polynomials Legendre's equation Ln(x obtain P₁(x polynomial of degree power series PROOF prove recurrence relation required result result of theorem right-hand side roots s₁ satisfies second kind series solutions Show sin² solution is given solution of equation theorem 4.8 Tn(x Un(x values xn+1 y₁(x Yn(x zero ηπ νπ π π χη