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Abstract
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The function
has the
well-known limit
as
. The coefficients
in an asymptotic
expansion for
are considered. A simple recursion formula is derived, and then using
Cauchy’s integral formula the coefficients are approximated for large
. From this it
is shown that
as
.
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Keywords
series expansions, asymptotic representations in the
complex plane, integrals of Cauchy type
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Mathematical Subject Classification
Primary: 41A58, 30E15, 30E20
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Milestones
Received: 12 May 2020
Accepted: 8 May 2021
Published: 9 February 2022
Communicated by Kenneth S. Berenhaut
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