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
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
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 Vladimir Nabokov＇s novel Lolita, we can find that Humbert tries to defend himself for his relation with Lolita. Humbert says Lolita has a precursor that is Annabel. That is pure love between children. Pure love is...In Vladimir Nabokov＇s novel Lolita, we can find that Humbert tries to defend himself for his relation with Lolita. Humbert says Lolita has a precursor that is Annabel. That is pure love between children. Pure love is innocent, so Humbert wants to say he is not to blame. His relation with Lolita is pure love. In addition, Edgar Allan Poe wrote a poem about Annabel Lee. And Humbert wants to say that it is the poem that makes him love Lolita.展开更多
Being criticized as the"deviant"literary works by mass people after being published, A Dream of Red Mansions and Lolita not only make great contribution to their source language literature history, but also ...Being criticized as the"deviant"literary works by mass people after being published, A Dream of Red Mansions and Lolita not only make great contribution to their source language literature history, but also enjoy indelible value in the literary field world-wide. In this paper, the writer makes a comparison between the two works with the heroes as a starting point from the abnormal loveview of the two heroes, the duality of the two heroes and the disillusion of their emotional utopiaso as to reflect the time-crossingresonances.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 Vladimir Nabokov＇s novel Lolita, we can find that Humbert tries to defend himself for his relation with Lolita. Humbert says Lolita has a precursor that is Annabel. That is pure love between children. Pure love is innocent, so Humbert wants to say he is not to blame. His relation with Lolita is pure love. In addition, Edgar Allan Poe wrote a poem about Annabel Lee. And Humbert wants to say that it is the poem that makes him love Lolita.
文摘Being criticized as the"deviant"literary works by mass people after being published, A Dream of Red Mansions and Lolita not only make great contribution to their source language literature history, but also enjoy indelible value in the literary field world-wide. In this paper, the writer makes a comparison between the two works with the heroes as a starting point from the abnormal loveview of the two heroes, the duality of the two heroes and the disillusion of their emotional utopiaso as to reflect the time-crossingresonances.
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.
