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math.CA2018★ 17 cited
Asymptotic expansions for the incomplete gamma function in the transition regions
Gergő Nemes, Adri B. Olde Daalhuis
We construct asymptotic expansions for the normalised incomplete gamma function that are valid in the transition regions, including the case , and…
math.CA2018★ 5 cited
An extension of Laplace's method
Gergő Nemes
Asymptotic expansions are obtained for contour integrals of the form \[ \int_a^b \exp \left( - zp(t) + z^{ν/μ} r(t) \right)q(t)dt, \] in which is a large real or complex parame…