In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma fu...In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].展开更多
The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fiel...Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.展开更多
The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several ...The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several special cases have been deducted.展开更多
This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, ev...This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, evolution, structure, ultimate fate, and primary parameters of the World. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the world and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;gamma-ray background and cosmic neutrino background;macrostructure of the world and macroobjects structure. Additionally, the model makes predictions pertaining to masses of dark matter particles, photons, and neutrinos, proposes new types of particle interactions (Super Weak and Extremely Weak), and shows inter-connectivity of primary cosmological parameters of the world and the rise of the solar luminosity during the last 4.6 Byr. The model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values.展开更多
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
文摘In this paper, the q-analogue of the Stirling formula for the q-gamma function （Moak formula） is exploited to prove the complete monotonicity properties of some functions involving the q-gamma and the q-polygamma functions for all real number q 〉 0. The monotonicity of these functions is used to establish sharp inequalities for the q-gamma and the q-polygamma functions and the q-Harmonic number. Our results are shown to be a generalization of results which were obtained by Selvi and Batir [23].
基金Supported by the National Natural Science Foundation of China（10771093） Supported by the Youth Foundation of Luoyang Normal College（2013-QNJJ-001） Supported by the Youth Foundation of the Luoyang Institute of Science and Technology（2012QZ05）
文摘The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.
文摘Generalized q-exponentials functions are employed to make a generalization of complete and incomplete gamma functions. We obtain a generalization of this class of special functions which are very important in the fields of probability, statistics, statistical physics as well as combinatorics and we derive some of its properties. One gets that the generalized gamma function obtained whether approaches of the standard gamma function for a specific q values such as q=q0≈0.9 value suffering a large variation with the variation of q.
文摘The present paper deals with the evaluation of the q-Analogues of Laplece transforms of a product of basic analogues of q2-special functions. We apply these transforms to three families of q-Bessel functions. Several special cases have been deducted.
文摘This paper provides an overview of the Hypersphere World-Universe Model (WUM). WUM unifies and simplifies existing cosmological models and results into a single coherent picture, and proceeds to discuss the origin, evolution, structure, ultimate fate, and primary parameters of the World. WUM explains the experimental data accumulated in the field of Cosmology and Astroparticle Physics over the last decades: the age of the world and critical energy density;the gravitational parameter and Hubble’s parameter;temperatures of the cosmic microwave background radiation and the peak of the far-infrared background radiation;gamma-ray background and cosmic neutrino background;macrostructure of the world and macroobjects structure. Additionally, the model makes predictions pertaining to masses of dark matter particles, photons, and neutrinos, proposes new types of particle interactions (Super Weak and Extremely Weak), and shows inter-connectivity of primary cosmological parameters of the world and the rise of the solar luminosity during the last 4.6 Byr. The model proposes to introduce a new fundamental parameter Q in the CODATA internationally recommended values.
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.
