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NOTE ON MULTIPLE q-ZETA FUNCTIONS

T. Kim|D. V. Dolgy|장관우
장전수학회 (Jangjeon Mathematical Society)|2017.01|Advanced Studies in Contemporary Mathematics|제27권 제1호|pp. 147-154|DOI 10.17777/ascm2017.27.1.147

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키워드

q-Euler numbersLaurent seriesmultiple q-zeta functionCauchy integral
주제분류수학

초록

In this paper we consider the analytic continuation of the multiple Euler q-zeta function in the complex number field as follows: ζEr,q(s,x)=[2]rq∞∑m1,…,mr=0(-1)m1+…+mr/[x+m1+…+mr]sq, where q ∈ C with |q| < 1, ℜ(x) > 0, and r ∈ N. Thus, we investigate their behavior near the poles and give the corresponding functional equations.

Abstract

In this paper we consider the analytic continuation of the multiple Euler q-zeta function in the complex number field as follows: ζEr,q(s,x)=[2]rq∞∑m1,…,mr=0(-1)m1+…+mr/[x+m1+…+mr]sq, where q ∈ C with |q| < 1, ℜ(x) > 0, and r ∈ N. Thus, we investigate their behavior near the poles and give the corresponding functional equations.

참고문헌 (23)

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관련 논문AI추천

ON THE TWISTED q-EULER ZETA FUNCTION ASSOCIATED WITH TWISTED q-EULER NUMBERS김영희, 김원주, 유천성장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제1호A note on the twisted Lerch type Euler zeta functions김대산, 서종진, Wenpeng Zhang, Yuan He대한수학회 · 대한수학회보2013 · 제50권 제2호Analytic continuation of weighted q-Genocchi numbers and polynomialsAynur Gursul, Mehmet Acikgoz, Serkan Araci대한수학회 · 대한수학회논문집2013 · 제28권 제3호ON THE q-EXTENSIONS OF THE BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND LERCH ZETA FUNCTION김영희, 김태균, 황경원장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2009 · 제12권 제1호Unification of multiple Lerch zeta type functionsA. Ahmet Aygunes, Yilmaz Simsek장전수학회 · Advanced Studies in Contemporary Mathematics2011 · 제21권 제4호q-analogues of some results for the Apostol-Euler polynomialsQiu-Ming Luo장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제1호

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