Liu Guo-Dong
Abstract
In this paper, we prove two explicit formulas for degenerate Bernoulli numbers and polynomials of higher order, and obtain an identity involving Bernoulli numbers of higher order and Stirling numbers. We extend and improve the results of F.H.Howard~[1], S.Shirai and K.I.Sato~[7].
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In this paper, we prove two explicit formulas for degenerate Bernoulli numbers and polynomials of higher order, and obtain an identity involving Bernoulli numbers of higher order and Stirling numbers. We extend and improve the results of F.H.Howard~[1], S.Shirai and K.I.Sato~[7].
Key concepts: Mathematics, Bernoulli number, Bernoulli polynomials, Stirling numbers of the second kind, Degenerate energy levels, Stirling number, Order (exchange), Identity (music)