Degenerate Bernoulli polynomials, generalized factorial sums, and their applications |
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Authors: | Paul Thomas Young |
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Affiliation: | Department of Mathematics, College of Charleston, Charleston, SC 29424, USA |
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Abstract: | We prove a general symmetric identity involving the degenerate Bernoulli polynomials and sums of generalized falling factorials, which unifies several known identities for Bernoulli and degenerate Bernoulli numbers and polynomials. We use this identity to describe some combinatorial relations between these polynomials and generalized factorial sums. As further applications we derive several identities, recurrences, and congruences involving the Bernoulli numbers, degenerate Bernoulli numbers, generalized factorial sums, Stirling numbers of the first kind, Bernoulli numbers of higher order, and Bernoulli numbers of the second kind. |
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Keywords: | Bernoulli numbers Degenerate Bernoulli numbers Power sum polynomials Generalized factorials Stirling numbers of first kind Bernoulli numbers of second kind |
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