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Asymptotic expansion of a series of Ramanujan

Published online by Cambridge University Press:  20 January 2009

Bruce C. Berndt  and
Ronald J. Evans
Bruce C. Berndt
Affiliation:
Department of Mathematics1409 West Green StreetUniversity of IllinoisUrbana, IL 61801
Ronald J. Evans
Affiliation:
Department of MathematicsUniversity of California, San DiegoLa Jolla, CA 92093–0112
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Abstract

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An asymptotic expansion is given for the series

as x→∞ in the sector |Argx|≦π/2–δ. Here δ, Re(a), and Re(s) are positive and r is a positive integer. In the case a = r = s = 1, this yields the nontrivial result

stated by Ramanujan in his notebooks [6].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 2 , June 1992 , pp. 189 - 199
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

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