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Special Functions: Course Outline (MAT 453)

Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.

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), Fourier-Legendre expansion, Laguerres differential equation, Strum Liouville equation ; orthogonality ; orthogonality of eigen-functions.

Reference Books

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