Listar Artículos de revista INAMAT2 - INAMAT2 aldizkari artikuluak por autor UPNA "Pérez Sinusía, Ester"
Mostrando ítems 1-13 de 13
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Analysis of singular one-dimensional linear boundary value problems using two-point Taylor expansions
We consider the second-order linear differential equation (x2 − 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 ... -
Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
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. ... -
An asymptotic expansion of the hyberbolic umbilic catastrophe integral
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
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 ... -
Convergent and asymptotic methods for second-order difference equations with a large parameter
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 ... -
A convergent version of Watson’s lemma for double integrals
A modification of Watson’s lemma for Laplace transforms ∞ 0 f(t) e−zt dt was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large |z| with the extra property of being convergent as well. Inspired ... -
New series expansions for the ℋ-function of communication theory
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 ... -
The swallowtail integral in the highly oscillatory region II
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
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 ... -
Uniform convergent expansions of the error function in terms of elementary functions
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) ... -
Uniform convergent expansions of the Gauss hypergeometric function in terms of elementary functions
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 ... -
Uniform representation of the incomplete beta function in terms of elementary functions
We consider the incomplete beta function Bz(a, b) in the maximum domain of analyticity of its three variables: a, b, z ∈ C, −a /∈ N, z /∈ [1, ∞). For <b ≤ 1 we derive a convergent expansion of z−aBz(a, b) in terms of the ... -
The use of two-point Taylor expansions in singular one-dimensional boundary value problems I
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 ...