相关论文: A q-analogue of the four functions theorem
A $q$-analogue of the multiple gamma functions is introduced, and is shown to satisfy the generalized Bohr-Morellup theorem. Furthermore we give some expressions of these function.
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
In this, paper we obtain a q-analogue of a double inequality involving the Euler gamma function which was first proved geometrically by Alsina and Tomas and then analytically by Sandor
Recently, Straub gave an interesting $q$-analogue of a binomial congruence of Ljunggren. In this note we give an inductive proof of his result.
We give a q-analogue of Gauss' divisibility theorem
We construct the q-analogue of Euler-Barnes' numbers and polynomials, and investigate their some properties.
We give q-analogues of Wilson's theorem for the primes congruent 1 and 3 modulo 4 respectively. And q-analogues of two congruences due to Mordell and Chowla are also established.
In this paper, we state some $q$-analogues of the famous Ramanujan's Master Theorem. As applications, some values of Jackson's $q$-integrals involving $q$-special functions are computed.
Recently (see [1]) I has introduced an interesting the Euler-Barnes multiple zeta function. In this paper we construct the q-analogue of Euler-Barnes multiple zeta function which interpolates the q-analogue of Frobenius-Euler numbers of…
Following an idea due to J. Bernoulli, we explore the q-analogue of the sums of powers of consecutive integers.
We propose a $q$-analog of classical plethystic conjectures due to Foulkes. In our conjectures, a divided difference of plethysms of Hall-Littlewood polynomials $H_n(\mathbf{x};q)$ replaces the analogous difference of plethysms of complete…
In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.
The additive analogues of Pseudo-Smarandache, Smarandache-simple functions and their duals have been recently studied by J. Sandor. In this note, we obtain q-analogue of Sandor's theorems.
In this work we shall apply the Bochner's theorem to prove certain combinations of Euler's q-exponentials are positive definite functions. Then we apply this positivity to prove curious inequalities for the Jacobi theta function…
We prove orthogonality relations for some analogs of trigonometric functions on a $q$-quadratic grid and introduce the corresponding $q$-Fourier series. We also discuss several other properties of this basic trigonometric system and the…
In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
In a 2016 ArXiv posting F. Bergeron listed a variety of symmetric functions $G[X;q]$ with the property that $G[X;1+q]$ is $e$-positive. A large subvariety of his examples could be explained by the conjecture that the Dyck path LLT…
Andrews once gave $q$-analogues of a binomial congruence of Glaisher, and he suggested perfect $q$-analogues. In this note we give ones meeting the demand of Andrews.
A q-difference analogue of the fourth Painlev\'e equation is proposed. Its symmetry structure and some particular solutions are investigated.