Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules

1993 ◽  
Vol 45 (3) ◽  
pp. 467-475 ◽  
Author(s):  
Gaoyuan Wei ◽  
B. E. Eichinger
Keyword(s):  
Asymptotic Expansions ◽  
Hypergeometric Functions ◽  
Matrix Argument

scholarly journals Uniform asymptotic expansions for the Whittaker functions M κ , μ ( z ) and W κ , μ ( z ) with μ large

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210360
Author(s):  
T. M. Dunster
Keyword(s):  
Analytic Continuation ◽  
Error Bounds ◽  
Asymptotic Expansions ◽  
Hypergeometric Functions ◽  
Whittaker Functions ◽  
Airy Functions ◽  
Elementary Functions ◽  
Confluent Hypergeometric Functions ◽  
Uniform Asymptotic Expansions

Uniform asymptotic expansions are derived for Whittaker’s confluent hypergeometric functions M κ , μ ( z ) and W κ , μ ( z ) , as well as the numerically satisfactory companion function W − κ , μ ( z   e − π i ) . The expansions are uniformly valid for μ → ∞ , 0 ≤ κ / μ ≤ 1 − δ < 1 and 0 ≤ arg ⁡ ( z ) ≤ π . By using appropriate connection and analytic continuation formulae, these expansions can be extended to all unbounded non-zero complex z . The approximations come from recent asymptotic expansions involving elementary functions and Airy functions, and explicit error bounds are either provided or available.

Hypergeometric Functions of 2 × 2 Matrix Argument are Expressible in Terms of Appell's Functions F 4

1978 ◽  
Vol 70 (1) ◽  
pp. 39
Author(s):  
Tom Koornwinder ◽  
Ida Sprinkhuizen-Kuyper
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Argument

scholarly journals On asymptotic expansions for functions of matrix argument

1979 ◽  
Vol 25 (2) ◽  
pp. 93-104 ◽  
Author(s):  
Yudell L Luke ◽  
G.P Barker
Keyword(s):  
Asymptotic Expansions ◽  
Matrix Argument

scholarly journals Expressions for some hypergeometric functions of matrix argument with applications

1975 ◽  
Vol 5 (3) ◽  
pp. 283-293 ◽  
Author(s):  
Robb J. Muirhead
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Argument

scholarly journals Extended k-Gamma and k-Beta Functions of Matrix Arguments

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1715
Author(s):  
Ghazi S. Khammash ◽  
Praveen Agarwal ◽  
Junesang Choi
Keyword(s):  
Gamma Function ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Formula ◽  
Beta Function ◽  
Integral Representations ◽  
Matrix Argument ◽  
Functional Relations

Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

scholarly journals Laplace approximations for hypergeometric functions with matrix argument

2002 ◽  
Vol 30 (4) ◽  
pp. 1155-1177 ◽  
Author(s):  
Roland W. Butler ◽  
Andrew T. A. Wood
Keyword(s):  
Hypergeometric Functions ◽  
Matrix Argument

UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I

2003 ◽  
Vol 01 (01) ◽  
pp. 111-120 ◽  
Author(s):  
A. B. OLDE DAALHUIS
Keyword(s):  
Asymptotic Expansion ◽  
Hypergeometric Function ◽  
Asymptotic Expansions ◽  
Hypergeometric Functions ◽  
Gauss Hypergeometric Function ◽  
Uniform Asymptotic Expansions

In this paper, we obtain an asymptotic expansion for the Gauss hypergeometric function 2F1(a, b - λ; c + λ; -z), as |λ| → ∞. The expansion holds for fixed values of a, b, and c, and is uniformly valid for z in the domain | ph z| < π.

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