Open AccessAn Exponential Matrix Product Based Representation for Generalized Hypergeometric Functions of Type p F p
Author(s) -
Baykara N. A.,
Yaman İrem,
Demiralp Metin
Publication year - 2005
Publication title -
applied numerical analysis & computational mathematics
Language(s) - English
Resource type - Journals
eISSN - 1611-8189
pISSN - 1611-8170
DOI - 10.1002/anac.200410020
Subject(s) - mathematics , frobenius solution to the hypergeometric equation , generalized hypergeometric function , confluent hypergeometric function , matrix (chemical analysis) , hypergeometric function , differential equation , hypergeometric identity , basic hypergeometric series , hypergeometric distribution , hypergeometric function of a matrix argument , truncation (statistics) , representation (politics) , mathematical analysis , exponential function , pure mathematics , political science , law , composite material , materials science , politics , statistics
In this work, a new representation is developed for generalized hypergeometric functions of type p F p . To this end a first order vector differential equation is constructed in a way such that the derivative of the unknown vector has unit matrix coefficient. The solution vector differential equation is rewritten in the form of a series expansion. An infinite process of factor extractions and annihilations is employed to construct finally a vector differential equation that can be easily solved. Truncation of this scheme can be used to get approximations to hypergeometric functions of type p F p . A simple, yet meaningful, implementation seems to give quite promising results. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)