2 citations · 10 across the 19 of their papers we have counts for
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The asymptotic expansion of Kratzel's integral and an integral related to an extension of the Whittaker function
R B Paris
We consider the asymptotic expansion of Krätzel's integral \[F_{p,ν}(x)=\int_0^\infty t^{ν-1} e^{-t^p-x/t}\,dt\qquad (|\arg\,x|<π/2),\] for as in the sector $…
The asymptotic expansion of a Mathieu-exponential series
R B Paris
We consider the asymptotic expansion of the functional series \[S_μ^\pm(a;λ)=\sum_{n=0}^\infty \frac{(\pm 1)^n e^{-λn}}{(n^2+a^2)^μ}\] for and as in…
A uniform asymptotic expansion for the incomplete gamma functions revisited
R B Paris
A new uniform asymptotic expansion for the incomplete gamma function valid for large values of was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002)…
Asymptotics of a Gauss hypergeometric function with large parameters, III: Application to the Legendre functions of large imaginary order and real degree
R. B. Paris
We obtain the asymptotic expansion for the Gauss hypergeometric function \[F(a-λ,b+λ;c+iαλ;z)\] for with , and finite parameters by application of…
A derivation of two transformation formulas contiguous to that of Kummer's second theorem via a differential equation approach
S. Kodavanji, A. K. Rathie, R. B. Paris
The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer's second transformation for the confluent hypergeometric fun…
A Poisson-Jacobi-type transformation for the sum $\sum_{n=1}^\infty n^{-2m} \exp (-an^2}$ for positive integer
R. B. Paris
We obtain an asymptotic expansion for the sum \[S(a;w)=\sum_{n=1}^\infty \frac{e^{-an^2}}{n^{w}}\] as in for arbitrary finite . The result whe…