A. Daalhuis

activity

20172024

most citedAsymptotic expansions for the incomplete gamma function in the transition regions

17 citations · 41 across the 4 of their papers we have counts for

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math.CA2024

Exponentially-improved asymptotics for $q$ -difference equations: $_{2} ϕ_{0}$ and $q P_{I}$

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…

math.CA2019★ 11 cited

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 $P_{ν}^{μ} (z)$ and $Q_{ν}^{μ} (z)$ for large degree $ν$ or large order $μ$ ar…

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 $Q (a, z) = Γ (a, z) /Γ (a)$ that are valid in the transition regions, including the case $z \approx a$ , and…

math.CA2017★ 13 cited

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…

Exponentially-improved asymptotics for q-difference equations: 2​ϕ0​ and qPI​

Large-parameter asymptotic expansions for the Legendre and allied functions

Asymptotic expansions for the incomplete gamma function in the transition regions

Globally exact asymptotics for integrals with arbitrary order saddles

Exponentially-improved asymptotics for $q$ -difference equations: $_{2} ϕ_{0}$ and $q P_{I}$