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    Shirasaka, S. 2002. On the Laurent coefficients of a class of Dirichlet series. Results in Mathematics, Vol. 42, Issue. 1-2, p. 128.


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  • Bulletin of the Australian Mathematical Society, Volume 33, Issue 3
  • June 1986, pp. 351-357

Laurent expansion of Dirichlet series

  • U. Balakrishnan (a1)
  • DOI: http://dx.doi.org/10.1017/S0004972700003919
  • Published online: 01 April 2009
Abstract

Let 〈an〉 be an increasing sequence of real numbers and 〈bn a sequence of positive real numbers. We deal here with the Dirichlet series and its Laurent expansion at the abscissa of convergence, λ, say. When an and bn behave like

as N → ∞, where P2(x) is a certain polynomial, we obtain the Laurent expansion of f (s) at s = λ, namely

where P1(x) is a polynomial connected with P2(x) above. Also, the connection between P1 and P2 is made intuitively transparent in the proof.

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[2]B.C. Berndt , ‘On the Hurwitz zeta function’, Rocky mountain J. Math., 2 (1972), 151157.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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