Browsing by UPNA Author "López García, José Luis"
Now showing items 1-20 of 41
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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 ... -
Analytic formulas for the evaluation of the Pearcey integral
We can find in the literature several convergent and/or asymptotic expansions of the Pearcey integral P(x, y) in different regions of the complex variables x and y, but they do not cover the whole complex x and y ... -
An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions
We derive new convergent expansions of the symmetric standard elliptic integral RD(x,y,z), for x,y,z∈C∖(−∞,0], in terms of elementary functions. The expansions hold uniformly for large and small values of one of the three ... -
Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter
In previous papers [6–8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not ... -
Asymptotic behaviour of the Urbanik semigroup
We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c ... -
The asymptotic expansion of the swallowtail integral in the highly oscillatory region
The mathematical models of many short wavelength phenomena, specially wave propagation and optical diffraction, contain, as a basic ingredient, oscillatory integrals with several nearly coincident stationary phase or ... -
Convergent and asymptotic expansions of solutions of differential equations with a large parameter: Olver cases II and III
This paper continues the investigation initiated in [Lopez, 2013]. We consider the asymptotic method designed by F. Olver [Olver, 1974] for linear differential equations of the second order containing a large (asymptotic) ... -
Convergent and asymptotic expansions of the Pearcey integral
We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels ... -
A convergent and asymptotic Laplace method for integrals
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 ... -
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 ... -
Convergent asymptotic expansions of Charlier, Laguerre and Jacobi polynomials
Convergent expansions are derived for three types of orthogonal polynomials: Charlier, Laguerre and Jacobi. The expansions have asymptotic properties for large values of the degree. The expansions are given in terms of ... -
Convergent expansions of the Bessel functions in terms of elementary functions
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of (sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives ... -
Convergent expansions of the confluent hypergeometric functions in terms of elementary functions
We consider the confluent hypergeometric function M(a, b; z) for z ∈ C and Rb >Ra > 0, and the confluent hypergeometric function U(a, b; z) for b ∈ C, Ra > 0, and Rz > 0. We derive two convergent expansions of M(a, b; z); ... -
Convergent expansions of the incomplete gamma functions in terms of elementary functions
We consider the incomplete gamma function γ(a,z) for Ra>0 and z∈C. We derive several convergent expansions of z−aγ(a,z) in terms of exponentials and rational functions of z that hold uniformly in z with Rz bounded from ... -
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 ... -
Effect of high-energy ball-milling on the magnetostructural properties of a Ni45Co5Mn35Sn15 alloy
(Elsevier, 2021) Artículo / ArtikuluaThe 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 ... -
An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions
In this paper we investigate the extension of the multiple Erd elyi-Kober fractional integral operator of Kiryakova to arbitrary complex values of parameters by the way of regularization. The regularization involves ... -
Formulas for the amplitude of the van der Pol limit cycle through the homotopy analysis method
The limit cycle of the van der Pol oscillator, x¨+ε(x2−1)x˙+x=0, is studied in the plane (x,x˙) by applying the homotopy analysis method. A recursive set of formulas that approximate the amplitude and form of this limit ... -
Generalization of Zernike polynomials for regular portions of circles and ellipses
Zernike polynomials are commonly used to represent the wavefront phase on circular optical apertures, since they form a complete and orthonormal basis on the unit circle. Here, we present a generalization of this Zernike ... -
New analytic representations of the hypergeometric functions p+1Fp
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 ...