Abstract
In this paper, we introduce a new class of (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these polynomials. We establish summation formulas of these polynomials by summation techniques series. Furthermore, we consider some relationships for (p, q)-Fubini polynomials associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials and (p, q)-Stirling numbers of the second kind.
Highlights
During the last two decades, the theory of (p, q)-calculus has been discussed and investigated extensively by many mathematicians and physicists
Milovanovic et al [15] introduced a new generalization of Beta functions based on (p, q)-numbers and committed the integral modification of the generalized Bernstien polynomials
Further making use of the Cauchy product rule in the resultant expressions and comparing the like powers of t in the both sides of resultant equation, we find formulas (2.4)-(2.6)
Summary
During the last two decades , the theory of (p, q)-calculus has been discussed and investigated extensively by many mathematicians and physicists. Sadjang [20] developed several properties of the (p, q)-derivatives and the (p, q)-integrals and as an application gave two (p, q)-Taylor formulas for polynomials. Throughout this presentation, we use the following standard notions N = {1, 2, · · · }, N0 = {0, 1, 2, · · · } = N ∪ {0}, Z− = {−1, −2, · · · }. We can write that [n]p,q = pn−1[n]q/p, where [n]q/p is the q-number in q-calculus given by [n]q/p (q/p)n −1 (q/p)−1.
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