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SPECIAL VALUES OF LERCH ZETA FUNCTION AND THEIR FOURIER EXPANSIONS

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초록

We prove a Fourier expansion for Lerch zeta transcendent ©. The special values of this zeta function at s = ¡n negative integers give us the so-called Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. Others applications are given.

Abstract

We prove a Fourier expansion for Lerch zeta transcendent ©. The special values of this zeta function at s = ¡n negative integers give us the so-called Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. Others applications are given.

참고문헌 (11)

  1. T.M.Apostol, "On the Lerch zeta function", Pacific J. Math, 1, pp.161~167 (1951)
  2. H.Bateman, "Higher Transcendental Functions, Vol. 1" (1953), McGraw-Hill
  3. R.Lipschitz, "Untersuchung der Eigenschaften einer Gattung von unendlichen Reihen", J. Reine und Angew. Math, 105, pp.127~156 (1889)
  4. 김태균, "ON THE q-EXTENSIONS OF THE BERNOULLI AND EULER NUMBERS, RELATED IDENTITIES AND LERCH ZETA FUNCTION", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 12(1), pp.77~92 (2009), 장전수학회
  5. K-W.Hwang, "Interpolation Functions of-Extensions of Apostol's Type Euler Polynomials", JOURNAL OF INEQUALITIES AND APPLICATIONS, pp.12~ (2009), HINDAWI PUBLISHING CORPORATION
  6. T.Kim, "On Euler-Barnes multiple zeta functions", Russ. J. Math. Phys, 10(3), pp.288~299 (2003)
  7. T.Kim, "Note on the Euler q-zeta functions", J. Number Theory, 129(7), pp.1798~1804 (2009)
  8. 김태균, "Note on Dedekind type DC sums", Advanced Studies in Contemporary Mathematics, 18(2), pp.249~260 (2009), 장전수학회
  9. H.Liu, "Some identities on the Bernoulli, Euler and Genocchi polynomials via power sums and alternate power sums", Discrete Math, 309(10), pp.3346~3363 (2009)
  10. Q-M.Luo, "Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials", Math. comp, 78(268), pp.2193~2208 (2009)
  11. P.C.Pasles, "A generalization of the Lipschitz summation formula and some applications", Proc. Amer. Math. Soc, 129, pp.3177~3184 (2001)

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