An extension of the Bernoulli polynomials inspired by the Tsallis statistics

2016/12/22 by M. Balamurugan, Balamurugan, M., Raj Chakrabarti +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Statistical Methods and Models #FOS: Physical sciences #Mathematical Physics (math-ph) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1612.07496

openalex publication_date 2016/12/22 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

In [Arch. Math. 7, 28 (1956), Utilitas Math. 15, 51 (1979)] Carlitz introduced the degenerate Bernoulli numbers and polynomials by replacing the exponential factors in the corresponding classical generating functions with their deformed analogs: exp(t) → (1+λt)^1/λ, and exp(tx) → (1+λt)^x/λ. The deformed exponentials reduce to their ordinary counterparts in the λ→ 0 limit. In the present work we study the extension of the Bernoulli polynomials obtained via an alternate deformation exp(tx) → (1+λtx)^1/λ that is inspired by the concepts of q-exponential function and q-logarithm used in the nonextensive Tsallis statistics.

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