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Asymptotic expansion of a series of Ramanujan
Published online by Cambridge University Press: 20 January 2009
Abstract
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].
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- Copyright © Edinburgh Mathematical Society 1992