Yoon Seok Choun

Grand Confluent Hypergeometric Function Applying Reversible Three-Term Recurrence Formula

abstract:
In this paper, by applying a reversible three-term recurrence formula (R3TRF) (see [13, Chapter 1]), we construct:
(1) power series expansions in closed forms of the grand confluent hypergeometric (GCH) equation,
(2) its integral forms for an infinite series and a polynomial which makes the leading non-constant coefficient on the RHS of the recurrence relation terminated,
(3) generating functions for GCH polynomials which makes the leading coefficient on the RHS terminated.

Mathematics Subject Classification: 33E20, 33E30, 34A99

Key words and phrases: Biconfluent Heun equation, generating function, integral form, reversible three-term recurrence formula