The aim of this paper is to define(p,q)-analogue of Mittag-Leffler Function,by using(p,q)-Gamma function.Some transformation formulae are also derived by using the(p,q)-derivative.The(p,q)-analogue for this function p...The aim of this paper is to define(p,q)-analogue of Mittag-Leffler Function,by using(p,q)-Gamma function.Some transformation formulae are also derived by using the(p,q)-derivative.The(p,q)-analogue for this function provides elegant generalization of q-analogue of Mittag-Leffler function in connection with q-calculus.Moreover,the(p,q)-Laplace Transform of the Mittag-Leffler function has been obtained.Some special cases have also been discussed.展开更多
With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations,called the Krattenthaler formulas.The present pap...With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations,called the Krattenthaler formulas.The present paper presents a very short proof of this formula via Lagrange interpolation. Further.our method of proof declares that the Krattenthaler result is unique in the light of Lagrange interpolation.展开更多
We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertw...We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertwining operators for natural representa- tions associated to Gel＇land spaces for our groups. This sequence and the sequence of their adjoint enable us to decompose in a recursive way these natural representations into irreducibles and to compute explicitly the associated spherical functions. Our methods and results rely then strongly on q-analogy.展开更多
The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relation...The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.展开更多
With the aid of the weight function of an r×r matrix associated with the symmetric group Sr of degree r, we obtain a direct method to determinate the addedfactor of multivariate Gould-Hsu inversion. Furthermore. ...With the aid of the weight function of an r×r matrix associated with the symmetric group Sr of degree r, we obtain a direct method to determinate the addedfactor of multivariate Gould-Hsu inversion. Furthermore. the q-analogue of this formula can also be derived by the same argument.展开更多
In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of ...In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.展开更多
基金温州大学硕士研究生创新基金资助项目“some q-analogue of alternating q-harmonic numbers and alternating q-supercongruence of modulo the cyclotomic polynomial”(3162023004054)。
文摘The aim of this paper is to define(p,q)-analogue of Mittag-Leffler Function,by using(p,q)-Gamma function.Some transformation formulae are also derived by using the(p,q)-derivative.The(p,q)-analogue for this function provides elegant generalization of q-analogue of Mittag-Leffler function in connection with q-calculus.Moreover,the(p,q)-Laplace Transform of the Mittag-Leffler function has been obtained.Some special cases have also been discussed.
文摘With an effort to investigate a unified approach to the Lagrange inverse Krattenthaler established operator method we finally found a general pair of inverse relations,called the Krattenthaler formulas.The present paper presents a very short proof of this formula via Lagrange interpolation. Further.our method of proof declares that the Krattenthaler result is unique in the light of Lagrange interpolation.
文摘We present a unified approach to the study of Radon transforms related to the group Sn and its q-analogue GLn（q）. In both cases, in a uniform way, we define a sequence of generMized Radon transforms that are intertwining operators for natural representa- tions associated to Gel＇land spaces for our groups. This sequence and the sequence of their adjoint enable us to decompose in a recursive way these natural representations into irreducibles and to compute explicitly the associated spherical functions. Our methods and results rely then strongly on q-analogy.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574060)the Natural Science Foundation of Liaocheng University of China (Grant No X071049)
文摘The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product （IWOP） of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S＇s（τ） │00） are investigated. It is found that, in different ranges of the squeezed parameter τ, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.
文摘With the aid of the weight function of an r×r matrix associated with the symmetric group Sr of degree r, we obtain a direct method to determinate the addedfactor of multivariate Gould-Hsu inversion. Furthermore. the q-analogue of this formula can also be derived by the same argument.
基金National Natural Science Foundation of China under Grant No.10574060the Natural Science Foundation of Shandong Province of China under Grant No.Y2004A09
文摘In this paper, in terms of the technique of integration within an ordered product （IWOP） of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. 3. Theor. Phys. 41 （2002） 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.
