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Barnes-type degenerate Bernoulli polynomials

T. Kim|D. V. Dolgy|김대산|T KOMATSU
장전수학회 (Jangjeon Mathematical Society)|2015.01|Advanced Studies in Contemporary Mathematics|제25권 제1호|pp. 121-146

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초록

In this paper, for any positive integer r, we consider the Barnes-type degenerate Bernoulli polynomials βn(λ, x|a1,...,ar) (a1,...,ar ≠ 0), generalizing the degener- ate Bernoulli polynomials βn(λ, x) (λ ≠ 0). From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.

Abstract

In this paper, for any positive integer r, we consider the Barnes-type degenerate Bernoulli polynomials βn(λ, x|a1,...,ar) (a1,...,ar ≠ 0), generalizing the degener- ate Bernoulli polynomials βn(λ, x) (λ ≠ 0). From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.

참고문헌 (13)

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  7. D. S. Kim, "Daehee polynomials with q-parameter", Adv. Studies Theor. Phys, 8(9), pp.423~445 (2014)
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  9. S. Roman, "The umbral Calculus" (2005), Dover
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  11. M. Wu, "Sums of products of the degenerate Euler numbers", Adv. Differ-ence Equ., 2014(40) (2014)
  12. P. T. Young, "Degenerate Bernoulli polynomials, generalized factorial sums and their applications", J. Number Theory, 128, pp.738~758 (2008)
  13. Z. Zhang, "On sums of products of the degenerate Bernoulli numbers", Integral Trans. Spec. Func, 20, pp.751~755 (2009)

관련 논문AI추천

BARNES' MULTIPLE BERNOULLI AND HERMITE MIXED-TYPE POLYNOMIALS김대산, 김태균, 임석훈, D. V. Dolgy장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2015 · 제18권 제1호SOME IDENTITIES OF THE DEGENERATE BERNOULLI POLYNOMIALS OF THE SECOND KIND ARISING FROM λ-SHEFFER SEQUENCES권종겸, 김병문, 박진우장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2021 · 제24권 제3호SOME IDENTITIES OF DEGENERATE POLY-q-BERNOULLI AND POLY-q-EULER POLYNOMIALS ARISING FROM λ -q-SHEFFER SEQUENCES김대산, 김태균, 김혜경장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제3호SOME PROPERTIES OF GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS AND NUMBERS권종겸, 김원주, Lee-Chae Jang장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제4호A NOTE ON DEGENERATE BERNOULLI POLYNOMIALS ARISING FROM UMBRAL CALCULUS박진우, 표성수장전수학회 · Advanced Studies in Contemporary Mathematics2022 · 제32권 제4호On the modified degenerate Bernoulli polynomials권혁인, 김태균, 서종진, DMITRY V. DOLGY장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제1호

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