21MAT436 SPECIAL FUNCTIONS-

Unit I-

Gamma and Beta Functions and Elliptic Functions

Unit II-

Special functions, power series solution of differential equations, ordinary point; Solution about singular points, Frobenius method, Bessel’s equation, solution of Bessel’s equation, Bessel’s functions Jn(x).

Unit III-

Recurrence Formulae, Equations reducible to Bessel’s equation, orthogonality of Bessel’s Functions, A generating function for Jn(x).

Unit IV-

Legendre’s equation, Legendre’s polynomial Pn(x), Legendre’s function of the second kind [Qn(x)], General solution of Legendre’s equation, Rodrigue’s formula, Legendre polynomials, A generating function of Legendre’s polynomial.

Unit V-

Orthogonality of Legendre polynomials, Recurrence formulae for Pn(x) Green’s function – Green’s Identities – Generalized functions.

TEXTBOOKS:
1) M.D. Raisinghania, Ordinary and Partial Differential Equations, S.Chand, 18th edition, 2016

REFERENCES:
1) I. N. Sneddon – Special Functions of mathematical Physics & Chemistry, 3 Oliver & Boyd, London.
2) N. N. Lebedev – Special Functions and Their Applications, PHI.
3) Special Functions, R. Askey and R. Roy, Cambridge.