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NOTE ON λ-LINEAR FUNCTION ARISING FROM THE p-ADIC FERMIONIC INTEGRAL ON Zp

김혜경|이대식
장전수학회 (Jangjeon Mathematical Society)|2022.04|Advanced Studies in Contemporary Mathematics|제32권 제2호|pp. 147-156

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참고문헌

키워드

p-adic invariant integralDegenerate Euler polynomialsDegenerate Euler polynomials of order rarising from the p-adic fermionic integralλ-umbral calculus
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초록

The p-adic Fermionic integral over Zp is one of the im- portant techniques among the many ways to investigate and construct generating functions for special polynomials and numbers. In this paper, we consider two λ-linear functionals on Cp[x] arising from the p-adic fermionic integral on Zp and Zrp = Zp×… Zp, re- spectively, by using umbral calculus and λ-umbral calculus. In other word, we study to determine the linear functionals given by P(x)→∫Zp P(x)dμ-1(x) and P(x)→∫Zp… ∫ZpP(x1+…+xr)dμ-1(x1)…dμ-4(XR), respectively.

Abstract

The p-adic Fermionic integral over Zp is one of the im- portant techniques among the many ways to investigate and construct generating functions for special polynomials and numbers. In this paper, we consider two λ-linear functionals on Cp[x] arising from the p-adic fermionic integral on Zp and Zrp = Zp×… Zp, re- spectively, by using umbral calculus and λ-umbral calculus. In other word, we study to determine the linear functionals given by P(x)→∫Zp P(x)dμ-1(x) and P(x)→∫Zp… ∫ZpP(x1+…+xr)dμ-1(x1)…dμ-4(XR), respectively.

참고문헌 (23)

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관련 논문AI추천

Linear functionals on the space of polynomials over CpD. S. Kim, H-I Kwon, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호p-adic q-integral on Zp associated with Frobenius-type Eulerian polynomials and umbral calculusD.S. Kim, H.Y. Lee, T. Kim장전수학회 · Advanced Studies in Contemporary Mathematics2013 · 제23권 제2호A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomialsM. Acikgoz, S. Araci장전수학회 · Advanced Studies in Contemporary Mathematics2012 · 제22권 제3호Symmetry identities for Changhee polynomials arising from the fermionic p-adic integral on Zp김태균, 서종진, D. V. Dolgy장전수학회 · Advanced Studies in Contemporary Mathematics2016 · 제26권 제2호On the analogs of Bernoulli and Euler numbers, related identities and zeta and L-functions김대열, 김태균, 임석훈, Yilmaz Simsek대한수학회 · 대한수학회지2008 · 제45권 제2호Degenerate Bernoulli numbers and polynomials associated with degenerate Hermite polynomialsHiba Haroon, Waseem Ahmad Khan대한수학회 · 대한수학회논문집2018 · 제33권 제2호

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