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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 ...
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 ...
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 approximations of the first symmetric elliptic integral in terms of elementary functions
(Springer, 2022)
info:eu-repo/semantics/article,
We consider the standard symmetric elliptic integral RF(x, y, z) for complex x, y, z. We derive convergent expansions of RF(x, y, z) in terms of elementary functions that hold uniformly for one of the three variables x, y ...
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 ...
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) ...
Effect of high-energy ball-milling on the magnetostructural properties of a Ni45Co5Mn35Sn15 alloy
(Elsevier, 2021)
info:eu-repo/semantics/article,
The effect of high-energy ball-milling on the magnetostructural properties of a Ni45Co5Mn35Sn15 alloy in austenitic phase at room temperature has been analyzed by neutron and high-resolution X-ray diffraction. The ball ...
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. ...
On a particular class of Meijer's G functions appearing in fractional calculus
(Academic Publications, 2018)
info:eu-repo/semantics/article,
In this paper we investigate the Meijer G-function G p+1,p+1 p,1 which, for certain parameter values, represents the Riemann-Liouville fractional integral of the Meijer-Nørlund function G p,p. p,0 The properties of this ...
Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp
(Taylor & Francis, 2020)
info:eu-repo/semantics/article,
We derive a convergent expansion of the generalized hypergeometric function p−1 F p in terms of the Bessel functions 0 F 1 that holds uniformly with respect to the argument in any horizontal strip of the complex plane. We ...