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Laurent expansion of Dirichlet series

Published online by Cambridge University Press:  17 April 2009

U. Balakrishnan
U. Balakrishnan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay – 5, India.
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Abstract

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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.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 351 - 357
Copyright
Copyright © Australian Mathematical Society 1986

References

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