Analytic solution for grand confluent hypergeometric function
Abstract
In previous paper I construct an approximative solution of the power series expansion in closed forms of Grand Confluent Hypergeometric (GCH) function only up to one term of A_n's [4]. And I obtain normalized constant and orthogonal relation of GCH function. In this paper I will apply three term recurrence formula [3] to the power series expansion in closed forms of GCH function (infinite series and polynomial) including all higher terms of A_n's. In general most of well-known special function with two recursive coefficients only has one eigenvalue for the polynomial case. However this new function with three recursive coefficients has infinite eigenvalues that make B_n's term terminated at specific value of index n because of three term recurrence formula [3]. This paper is 9th out of 10 in series "Special functions and three term recurrence formula (3TRF)". See section 6 for all the papers in the series. Previous paper in series deals with generating functions of Lame polynomial in the Weierstrass's form [28]. The next paper in the series describes the integral formalism and the generating function of GCH function [30].
Keywords
Cite
@article{arxiv.1303.0813,
title = {Analytic solution for grand confluent hypergeometric function},
author = {Yoon Seok Choun},
journal= {arXiv preprint arXiv:1303.0813},
year = {2014}
}
Comments
16 pages, final version. arXiv admin note: substantial text overlap with arXiv:1303.0819, arXiv:1303.0879, arXiv:1302.7309, arXiv:1303.0878, arXiv:1303.0876, arXiv:1303.0873