SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS

Basic theory of special functions: differential equations, polynomials of hypergeometric type-Rodriques' formula, integral representations of functions of hypergeometric type, recurrence relations and differentiation's formulae. Classic orthogonal polynomials: basic properties of polynomials of hypergeometric type, expansion of functions in series of classic orthogonal polynomials, eigenvalue problems whixh are solved by use of orthogonal polynomials, spherical harmonics. Functions of second kind. Orthogonal polynomials of a discrete variable in non-uniform lattices. Bessel functions: semi-classical approach (WKB method). Hypergeometric functions. Applications in the group representation theory and Mathematical Physics.