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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 ...
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) ...
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 ...
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., ...
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 use of two-point Taylor expansions in singular one-dimensional boundary value problems I
(Elsevier, 2018)
info:eu-repo/semantics/article,
We consider the second-order linear differential equation (x + 1)y′′ + f(x)y′ + g(x)y = h(x) in
the interval (−1, 1) with initial conditions or boundary conditions (Dirichlet, Neumann or mixed
Dirichlet-Neumann). The ...
Convergent and asymptotic methods for second-order difference equations with a large parameter
(Springer, 2018)
info:eu-repo/semantics/article,
We consider the second-order linear difference equation y(n+2)−2ay(n+1)−Λ2y(n)=g(n)y(n)+f(n)y(n+1) , where Λ is a large complex parameter, a≥0 and g and f are sequences of complex numbers. Two methods are proposed to find ...
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
(Taylor & Francis, 2018)
info:eu-repo/semantics/article,
We consider the hypergeometric function 2F1(a, b; c; z) for z ∈ C \ [1,∞). For Ra ≥ 0, we derive a convergent expansion of 2F1(a, b; c; z) in terms of the function (1 − z)−a and of rational functions of z that is uniformly ...