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CLOSED FORMS FOR DEGENERATE BERNOULLI POLYNOMIALS

Part of: Combinatorics Sequences and sets

Published online by Cambridge University Press:  10 January 2020

LEI DAI  and
HAO PAN
LEI DAI
Affiliation:
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing210046, PR China email [email protected]
HAO PAN*
Affiliation:
School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing210046, PR China email [email protected]
*
✉[email protected]
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Abstract

Qi and Chapman [‘Two closed forms for the Bernoulli polynomials’, J. Number Theory159 (2016), 89–100] gave a closed form expression for the Bernoulli polynomials as polynomials with coefficients involving Stirling numbers of the second kind. We extend the formula to the degenerate Bernoulli polynomials, replacing the Stirling numbers by degenerate Stirling numbers of the second kind.

Keywords

degenerate Bernoulli polynomialdegenerate Stirling number of the second kindBell polynomial

MSC classification

Primary: 11B68: Bernoulli and Euler numbers and polynomials
Secondary: 05A10: Factorials, binomial coefficients, combinatorial functions 11B65: Binomial coefficients; factorials; $q$-identities 11B73: Bell and Stirling numbers
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 207 - 217
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

The work is supported by the National Natural Science Foundation of China (Grant No. 11671197).

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