Symmetric Identities on Modified Degenerate Bernoulli Polynomials

Abstract:

The modified degenerate Bernoulli polynomial ${\mathfrak{B}}_{n,\lambda}(x)$ introduced by Dolgy et al. is given by

$\displaystyle \sum_{n=0}^\infty\frac{{\mathfrak{B}}_{n,\lambda}(x)}{n!}t^n=\frac{t(1+\lambda)^{\frac{xt}\lambda}}{(1+\lambda)^{\frac t\lambda}-1}.$

In this paper, we prove some symmetric identities on modified degenerate Bernoulli polynomials, which generalize the result of Fu, Pan, and Zhang.

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(Concerned with sequences A027641 A027642.)

Received August 27 2023; revised version received April 11 2024; April 24 2024. Published in Journal of Integer Sequences, May 12 2024.