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Partial differential equations for hypergeometric functions 3 F 2 of matrix argument
Author(s) -
Fujikoshi Yasunori
Publication year - 1975
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315276
Subject(s) - mathematics , hypergeometric function of a matrix argument , hypergeometric function , confluent hypergeometric function , hypergeometric distribution , matrix (chemical analysis) , pure mathematics , appell series , partial differential equation , differential equation , argument (complex analysis) , generalized hypergeometric function , mathematical physics , mathematical analysis , biochemistry , chemistry , materials science , composite material
Many multivariate non‐null distributions and moment formulas can be expressed in terms of hypergeometric functions p F q of matrix arqument. Muirhead [6] and Constantine and Muirhead [2] gave partial differential equations for the functions of 2 F 1 of one argument matrix and two argument matrices, respectively. Such differential equations have been used to obtain asymptotic expansions of the functions (Muirhead [7], [8], [9], Sugiura [10]). The purpose of this paper is to derive partial differential equations for the functions 3 F 2 (a 1 a 2 , a 3 ; b 1 , b 2 , R) and 3 F 2 (a 1 , a 2 , a 3 ; b 1 , b 2 ; R, S). Differential equations for 2 F 2 are also obtained.