Explicit formula of a new class of q-Hermite-based Apostol-type polynomials and generalization

Abstract

The present article deals with a recent study of a new class of q-Hermite-based Apostol-type polynomials introduced by Waseem A. Khan and Divesh Srivastava. We give their explicit formula and study a generalized class depending in any q-analog generating function.

Untitled

“…For the general case 𝑔𝑜𝑓 one consult [6,8] , to see the 𝑞-analog we refer to [7] . According to Bell polynomials the expression of 𝑎 𝑛 (𝑚) as a polynomial on the integer variable 𝑚 is given in the following theorem.…”

On Bell polynomials associated to Vasyunin cotangent sums

“…For the proof we refer to [12] and references therein. Otherwise B n,k appear in the Faà di Bruno formula [8] for computing the n-th derivative of f • g. Let D n f the n-th derivative of f then…”