17 citations · 41 across the 4 of their papers we have counts for
4 papers
Exponentially-improved asymptotics for -difference equations: and
Nalini Joshi, Adri Olde Daalhuis
Usually when solving differential or difference equations via series solutions one encounters divergent series in which the coefficients grow like a factorial. Surprisingly, in the…
Large-parameter asymptotic expansions for the Legendre and allied functions
Gergő Nemes, Adri B. Olde Daalhuis
Surprisingly, apart from some special cases, simple asymptotic expansions for the associated Legendre functions and for large degree or large order ar…
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…
Globally exact asymptotics for integrals with arbitrary order saddles
Thomas Bennett, Christopher J. Howls, Gergő Nemes +1
We derive the first exact, rigorous but practical, globally valid remainder terms for asymptotic expansions about saddles and contour endpoints of arbitrary order degeneracy derive…