On some inequalities of uncertainty principles type in quantum calculus.
On some operational representations of -polynomials
On Some Partition Functions Related to Some Mock Theta Functions
We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.
On the Faraut-Koranyi hypergeometric functions in rank two
We give a complete description of the boundary behaviour of the generalized hypergeometric functions, introduced by Faraut and Koranyi, on Cartan domains of rank 2. The main tool is a new integral representation for some spherical polynomials, which may be of independent interest.
On the limit from -Racah polynomials to big -Jacobi polynomials.
On the non-quadraticity of values of the q-exponential function and related q-series
On the -analogue of gamma functions and related inequalities.
On the q-exponential of matrix q-Lie algebras
In this paper, we define several new concepts in the borderline between linear algebra, Lie groups and q-calculus.We first introduce the ring epimorphism r, the set of all inversions of the basis q, and then the important q-determinant and corresponding q-scalar products from an earlier paper. Then we discuss matrix q-Lie algebras with a modified q-addition, and compute the matrix q-exponential to form the corresponding n × n matrix, a so-called q-Lie group, or manifold, usually with q-determinant...
On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.
On the symmetries of the -Bernoulli polynomials.
Orthogonal polynomials and recurrence equations, operator equations and factorization.
Orthogonal -polynomials related to perturbed linear form.
Overpartition pairs
An overpartition pair is a combinatorial object associated with the -Gauss identity and the summation. In this paper, we prove identities for certain restricted overpartition pairs using Andrews’ theory of recurrences for well-poised basic hypergeometric series and the theory of Bailey chains.
Parameter augmentation for two formulas.
Partial sums of two quartic -series.
Partition statistics and -Bell numbers .
Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus
Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties of this function with proofs...
Probabilities as values of modular forms and continued fractions.
-analogue of Wright function.
-analogues of the sums of consecutive integers, squares, cubes, quarts and quints.