Special Functions: Course Outline (MAT 453)
Course Contents
Introduction, Gamma Functions, Beta Functions; Hyper geometric series, power series solution of differential equations, ordinary point, solution about singular point Frobenius method, Bessel's equation, solution of Bessel's equation; Bessel's functions, J (x), recurrence formulae, equations reducible to Bessel's equation, orthogonality of Bessel functions, a generating function of J (x), trigonometric expansion involving Bessel functions, Bessel integral, Ber and Bei functions, Legendres equation; Legendre's polynomial P_n (x); Legendre's function of the second kind; General solution of Legendre's Equation, Rodrigue's formula, Legendre polynomials, a generating function of Legendre's polynomial, Orthogonlity of Legendre polynomials; recurrence formulae for Ps(x), FourierLegendre expansion, Laguerres differential equation, Strum Liouville equation ; orthogonality ; orthogonality of eigenfunctions.
Reference Books

Elementary Applied Partial Differential Equations byCall Number: 515.35 HABISBN: 013263807XPublication Date: 1998

Ordinary and partial differential equations byCall Number: 515.352 RAIISBN: 9789385676161Publication Date: 2016
Other Books

by Collins, Peter J.
Date Published: 2006
Pages: 387 
by Emmrich, Etienne
Wittbold, Petra
Date Published: 2009