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Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
(Wiley, 2023)
Artículo / Artikulua,
We consider the highly oscillatory integral 𝐹(𝑤) ∶= ∫ ∞ −∞ 𝑒𝑖𝑤(𝑡𝐾+2+𝑒𝑖𝜃𝑡𝑝) 𝑔(𝑡)𝑑𝑡 for large positive values of 𝑤, −𝜋 < 𝜃 ≤ 𝜋, 𝐾 and 𝑝 positive integers with 1 ≤ 𝑝 ≤ 𝐾, and 𝑔(𝑡) an entire function. ...
Asymptotic expansions for Moench's integral transform of hydrology
(MDPI, 2023)
Artículo / Artikulua,
Theis' theory (1935), later improved by Hantush & Jacob (1955) and Moench (1971), is a technique designed to study the water level in aquifers. The key formula in this theory is a certain integral transform H[g](r,t) of ...
A convergent and asymptotic Laplace method for integrals
(Elsevier, 2023)
Artículo / Artikulua,
Watson’s lemma and Laplace’s method provide asymptotic expansions of Laplace integrals F (z) := ∫ ∞
0
e
−zf (t)
g(t)dt for large values of the parameter z. They are useful
tools in the asymptotic approximation of ...
Uniform convergent expansions of the error function in terms of elementary functions
(Springer, 2023)
Artículo / Artikulua,
We derive a new analytic representation of the error function erfz
in the form of a convergent series whose terms are exponential and rational functions. The expansion holds uniformly in z in the double sector | arg (±z) ...
New series expansions for the ℋ-function of communication theory
(Taylor & Francis, 2023)
Artículo / Artikulua,
TheH-function of communication theory plays an important role inthe error rate analysis in digital communication with the presenceof additive white Gaussian noise (AWGN) and generalized multipathfading conditions. In this ...