scholarly journals Properties of Matrix Variate Confluent Hypergeometric Function Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Arjun K. Gupta ◽  
Daya K. Nagar ◽  
Luz Estela Sánchez
Keyword(s):  
Hypergeometric Function ◽  
Random Matrices ◽  
Gamma Distribution ◽  
Confluent Hypergeometric Function ◽  
Density Functions ◽  
Function Distribution ◽  
Gamma Distributions ◽  
The Matrix

We study matrix variate confluent hypergeometric function kind 1 distribution which is a generalization of the matrix variate gamma distribution. We give several properties of this distribution. We also derive density functions ofX2-1/2X1X2-1/2,(X1+X2)-1/2X1(X1+X2)-1/2, andX1+X2, wherem×mindependent random matricesX1andX2follow confluent hypergeometric function kind 1 and gamma distributions, respectively.

scholarly journals Properties of Matrix Variate Beta Type 3 Distribution

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Arjun K. Gupta ◽  
Daya K. Nagar
Keyword(s):  
Probability Density ◽  
Hypergeometric Function ◽  
Random Matrices ◽  
Confluent Hypergeometric Function ◽  
Probability Density Functions ◽  
Density Functions ◽  
Type 3

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell's first hypergeometric functionF1and Humbert's confluent hypergeometric functionΦ1of matrix arguments. Further, a bimatrix variate generalization of the beta type 3 distribution is also defined and studied.

scholarly journals MATRIX-VARIATE GAUSS HYPERGEOMETRIC DISTRIBUTION

2012 ◽  
Vol 92 (3) ◽  
pp. 335-355 ◽  
Author(s):  
ARJUN K. GUPTA ◽  
DAYA K. NAGAR
Keyword(s):  
Probability Density ◽  
Hypergeometric Function ◽  
Random Matrices ◽  
Confluent Hypergeometric Function ◽  
Probability Density Functions ◽  
Hypergeometric Distribution ◽  
Density Functions

AbstractIn this paper, we propose a matrix-variate generalization of the Gauss hypergeometric distribution and study several of its properties. We also derive probability density functions of the product of two independent random matrices when one of them is Gauss hypergeometric. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric function Φ1of matrix arguments.

Bivariate Extended Confluent Hypergeometric Function Distribution

2013 ◽  
Vol 32 (2) ◽  
pp. 91-100
Author(s):  
Daya K. Nagar ◽  
Raúl Alejandro Morán-Vásquez ◽  
Alejandro Roldán-Correa
Keyword(s):  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Function Distribution

scholarly journals The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1273
Author(s):  
Alexander Apelblat ◽  
Armando Consiglio ◽  
Francesco Mainardi
Keyword(s):  
Hypergeometric Function ◽  
Laplace Transforms ◽  
Confluent Hypergeometric Function ◽  
Integral Function ◽  
Basic Properties ◽  
Differential Relations

The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature.

Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity, I

1984 ◽  
Vol 99 (1-2) ◽  
pp. 51-70 ◽  
Author(s):  
F. V. Atkinson ◽  
C. T. Fulton
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Hypergeometric Function ◽  
Finite Interval ◽  
Confluent Hypergeometric Function ◽  
Limit Circle ◽  
Asymptotic Formulae ◽  
Sturm Liouville

SynopsisAsymptotic formulae for the positive eigenvalues of a limit-circle eigenvalue problem for –y” + qy = λy on the finite interval (0, b] are obtained for potentials q which are limit circle and non-oscillatory at x = 0, under the assumption xq(x)∈L1(0,6). Potentials of the form q(x) = C/xk, 0<fc<2, are included. In the case where k = 1, an independent check based on the limit-circle theory of Fulton and an asymptotic expansion of the confluent hypergeometric function, M(a, b; z), verifies the main result.

A Generalised Kummer-Type Transformation for the pFp(x) Hypergeometric Function

2012 ◽  
Vol 55 (3) ◽  
pp. 571-578
Author(s):  
A. R. Miller ◽  
R. B. Paris
Keyword(s):  
Hypergeometric Function ◽  
Confluent Hypergeometric Function ◽  
Reduction Formula ◽  
Type Transformation

AbstractIn a recent paper, Miller derived a Kummer-type transformation for the generalised hypergeometric function pFp(x) when pairs of parameters differ by unity, by means of a reduction formula for a certain Kampé de Fériet function. An alternative and simpler derivation of this transformation is obtained here by application of the well-known Kummer transformation for the confluent hypergeometric function corresponding to p = 1.

scholarly journals An asymptotic property of large matrices with identically distributed Boolean independent entries

2019 ◽  
Vol 22 (04) ◽  
pp. 1950024
Author(s):  
Mihai Popa ◽  
Zhiwei Hao
Keyword(s):  
Recent Result ◽  
Recent Work ◽  
Random Matrices ◽  
Asymptotic Property ◽  
Limit Distribution ◽  
Asymptotic Independence ◽  
Moment Conditions ◽  
The Matrix ◽  
Combinatorial Condition ◽  
Independence Relations

Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean independent entries. More precisely, we show that, under some moment conditions, such random matrices are asymptotically [Formula: see text]-diagonal and Boolean independent from each other. This paper also gives a combinatorial condition under which such matrices are asymptotically Boolean independent from the matrix obtained by permuting the entries (thus extending a recent result in Boolean probability). In particular, we show that the random matrices considered are asymptotically Boolean independent from some of their partial transposes. The main results of the paper are based on combinatorial techniques.

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