Abstract
In this paper, we introduce new class of higher order hypergeometric Hermite-Bernoulli numbers and polynomials. We shall provide several properties of higher order hypergeometric Hermite-Bernoullipolynomials including summation formulae, sums of products identity, recurrence relations.
Highlights
Howard ( [5], [6]) gave a generalization of Bernoulli polynomials by considering the following generating function t2ext/2 et − 1 − t
We develop some elementary properties and derive the implicit summation formulae for the higher-order hypergeometric Hermite-Bernoulli polynomials by using different analytical means on their respective generating functions
The approach given in recent papers of Pathan and Khan ( [16][18]) has allowed the derivation of implicit summation formulae in the two-variable higher-order hypergeometric Hermite-Bernoulli polynomials
Summary
Howard ( [5], [6]) gave a generalization of Bernoulli polynomials by considering the following generating function t2ext/2 et − 1 − t. For N, r ∈ N, the higher-order hypergeometric Bernoulli polynomials BN(r,)n(x) are defined by means of the generating function, (see [2], [7], [10]) We develop some elementary properties and derive the implicit summation formulae for the higher-order hypergeometric Hermite-Bernoulli polynomials by using different analytical means on their respective generating functions.
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