-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.