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.
-Bernstein polynomials associated with -Stirling numbers and Carlitz's -Bernoulli numbers.
-Genocchi numbers and polynomials associated with -Genocchi-type -functions.
-Riemann zeta function.
q-Heat Operator and q-Poisson’s Operator
2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated with the q-operator ∆q (see[5]). We begin by summarizing some statements concerning the q-even translation operator Tx,q, defined by Fitouhi and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat semi-group such as boundedness and positivity. In the second part, we introduce the q-Poisson operator P^t, and address its main properties. We show...
Quantum Barnes function as the partition function of the resolved conifold.
Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions
Rogers-Ramanujan-Slater type identities.
Self-conjugate vector partitions and the parity of the spt-function
Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. Recently, we found new combinatorial interpretations of congruences for the spt-function modulo 5 and 7. These interpretations were in terms of a restricted set of weighted vector partitions which we call S-partitions. We prove that the number of self-conjugate S-partitions, counted with a certain weight, is related to the coefficients of a certain mock theta function studied by the first author,...
Séries de -factorielles, opérateurs aux -différences et confluence
Several -series identities from the Euler expansions of and
In this paper, we first give several operator identities which extend the results of Chen and Liu, then make use of them to two -series identities obtained by the Euler expansions of and . Several -series identities are obtained involving a -series identity in Ramanujan’s Lost Notebook.
Signed words and permutations. III: The MacMahon Verfahren.
Some explicit values for ratios of theta-functions.
Some new transformations for Bailey pairs and WP-Bailey pairs
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.