The main object of this paper is to deduce the bibasic Humbert functions Ξ_(1) and Ξ_(2)Some interesting results and elementary summations technique that was successfully employed,q-recursion,q-derivatives relations...The main object of this paper is to deduce the bibasic Humbert functions Ξ_(1) and Ξ_(2)Some interesting results and elementary summations technique that was successfully employed,q-recursion,q-derivatives relations,the q-differential recursion relations,the q-integral representations for Ξ_(1) and Ξ_(2)are given.The summation formula derives a list of p-analogues of transformation formulas for bibasic Humbert functions that have been studied,also some hypergeometric functions properties of some new interesting special cases have been given.展开更多
This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix functio...This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix function and Kummer matrix function is studied. Also, integral expressions of this relation are deduced. Finally, we define and study of the composite Humbert Kummer matrix functions.展开更多
In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansi...In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer ma-trix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables.展开更多
The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish so...The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish some new results and provide a discussion on computing methods on the distribution of the ratio: the largest eigenvalue to trace.展开更多
基金Supported by the National Natural Science Foundation of China(11601266)the Natural Science Foundation of Fujian Province of China(2020J01783)。
文摘The main object of this paper is to deduce the bibasic Humbert functions Ξ_(1) and Ξ_(2)Some interesting results and elementary summations technique that was successfully employed,q-recursion,q-derivatives relations,the q-differential recursion relations,the q-integral representations for Ξ_(1) and Ξ_(2)are given.The summation formula derives a list of p-analogues of transformation formulas for bibasic Humbert functions that have been studied,also some hypergeometric functions properties of some new interesting special cases have been given.
文摘This paper deals with the study of the composite Humbert matrix function with matrix arguments . The convergence and integral form this function is established. An operational relation between a Humbert matrix function and Kummer matrix function is studied. Also, integral expressions of this relation are deduced. Finally, we define and study of the composite Humbert Kummer matrix functions.
文摘In this paper we introduce Humbert matrix polynomials of two variables. Some hypergeometric matrix representations of the Humbert matrix polynomials of two variables, the double generating matrix functions and expansions of the Humbert matrix polynomials of two variables in series of Hermite polynomials are given. Results of Gegenbauer ma-trix polynomials of two variables follow as particular cases of Humbert matrix polynomials of two variables.
文摘The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish some new results and provide a discussion on computing methods on the distribution of the ratio: the largest eigenvalue to trace.
