Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions

通过分析生成函数,研究特殊数和高阶多项式的恒等式和递推关系

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Abstract

The aim of this is to give generating functions for new families of special numbers and polynomials of higher order. By using these generating functions and their functional equations, we derive identities and relations for these numbers and polynomials. Relations between these new families of special numbers and polynomials and Bernoulli numbers and polynomials are given. Finally, recurrence relations and derivative formulas, which are related to these numbers and polynomials, are given.

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