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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 recurrence relations for several classical families of polynomials
(Taylor and Francis, 2021)
info:eu-repo/semantics/article,
In this paper, we derive new recurrence relations for the following families of polynomials: nörlund polynomials, generalized Bernoulli polynomials, generalized Euler polynomials, Bernoulli polynomials of the second kind, ...
An asymptotic expansion of the hyberbolic umbilic catastrophe integral
(Springer, 2022)
Artículo / Artikulua,
We obtain an asymptotic expansion of the hyperbolic umbilic catastrophe integral Ψ(H) (x,y,z) := ∫∞−∞∫∞−∞exp(i(s3+t3+zst +yt+xs))ds dt
for large values of |x| and bounded values of |y| and |z|. The expansion is given ...
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 ...
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. ...
New analytic representations of the hypergeometric functions p+1Fp
(Springer, 2021)
info:eu-repo/semantics/article,
The power series expansions of the hypergeometric functions p+1Fp (a,b1,…,bp;c1,…,cp;z) converge either inside the unit disk |z|<1 or outside this disk |z|>1. Nørlund’s expansion in powers of z/(z−1) converges in the ...
Uniform convergent expansions of integral transforms
(American Mathematical Society, 2021)
info:eu-repo/semantics/article,
Several convergent expansions are available for most of the special functions of the mathematical physics, as well as some asymptotic expansions [NIST Handbook of Mathematical Functions, 2010]. Usually, both type of ...
The swallowtail integral in the highly oscillatory region III
(Taylor & Francis, 2021)
info:eu-repo/semantics/article,
We consider the swallowtail integral Ψ(x,y,z):=∫∞−∞ei(t5+xt3+yt2+zt)dt for large values of |z| and bounded values of |x| and |y|. The integrand of the swallowtail integral oscillates wildly in this region and the asymptotic ...
The swallowtail integral in the highly oscillatory region II
(Kent State UniversityJohann Radon Institute (RICAM), 2020)
info:eu-repo/semantics/article,
We analyze the asymptotic behavior of the swallowtail integral R ∞ −∞ e i(t 5+xt3+yt2+zt)dt for large values of |y| and bounded values of |x| and |z|. We use the simpli ed saddle point method introduced in [López et al., ...
Series representations of the Volterra function and the Fransén–Robinson constant
(Elsevier, 2021)
info:eu-repo/semantics/article,
The Volterra function μ(t,β,α) was introduced by Vito Volterra in 1916 as the solution to certain integral equations with a logarithmic kernel. Despite the large number of applications of the Volterra function, the only ...