# Person: López García, José Luis

Loading...

## Email Address

## Birth Date

## Research Projects

## Organizational Units

## Job Title

## Last Name

López García

## First Name

José Luis

## person.page.departamento

Estadística, Informática y Matemáticas

## person.page.instituteName

InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

## ORCID

0000-0002-6050-9015

## person.page.upna

2369

## Name

7 results Back to results

### Filters

#### Author

#### Date

#### Has files

#### Item Type

### Settings

Sort By

Results per page

## Search Results

Now showing 1 - 7 of 7

Publication Open Access A convergent version of Watson’s lemma for double integrals(Taylor & Francis, 2022) Ferreira González, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more 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 in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms F(x, y) := ∞ 0 ∞ 0 f(t,s) e−xt−ys dt ds for large |x| and |y| that are also convergent. The expansions of F(x, y) are accompanied by error bounds. Asymptotic and convergent expansions of some specialfunctions are given as illustration.Show more Publication Open Access The uniform asymptotic method "saddle point near an end point" revisited(Elsevier, 2024) López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertistate PublikoaShow more We continue the program initiated in [López & all, 2009–2011] to simplify asymptotic methods for integrals: in this paper we revise the uniform method ‘‘saddle point near an end point’’. We obtain a more systematic version of this uniform asymptotic method where the computation of the coefficients of the asymptotic expansion is remarkably simpler than in the classical method. On the other hand, as in the standard method, the asymptotic sequence is given in terms of parabolic cylinder functions. New asymptotic expansions of the confluent hypergeometric functions 𝑀(𝑐, 𝑥∕𝛼 + 𝑐 + 1, 𝑥) and 𝑈(𝑐, 𝛼𝑥 + 𝑐 + 1, 𝑥) for large 𝑥, 𝑐 fixed, uniformly valid for 𝛼 ∈ (0, ∞), are given as an illustration.Show more Publication Open Access Series representations of the Volterra function and the Fransén–Robinson constant(Elsevier, 2021) López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more 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 known analytic representations of this function are given in terms of integrals. In this paper we derive several convergent expansion of μ(t,β,α) in terms of incomplete gamma functions. These expansions may be used to implement numerical evaluation techniques for this function. As a particular application, we derive a numerical series representation of the Fransén–Robinson constant F := µ(1, 1, 0) = R ∞ 0 1 Γ(x) dx. Some numerical examples illustrate the accuracy of the approximationsShow more Publication Open Access Uniform convergent expansions of integral transforms(American Mathematical Society, 2021) López García, José Luis; Palacios Herrero, Pablo; Pagola Martínez, Pedro Jesús; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more 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 expansions are given in terms of elementary functions; the convergent expansions provide a good approximation for small values of a certain variable, whereas the asymptotic expansions provide a good approximation for large values of that variable. Also, quite often, those expansions are not uniform: the convergent expansions fail for large values of the variable and the asymptotic expansions fail for small values. In recent papers [Bujanda & all, 2018-2019] we have designed new expansions of certain special functions, given in terms of elementary functions, that are uniform in certain variables, providing good approximations of those special functions in large regions of the variables, in particular for large and small values of the variables. The technique used in [Bujanda & all, 2018-2019] is based on a suitable integral representation of the special function. In this paper we face the problem of designing a general theory of uniform approximations of special functions based on their integral representations. Then, we consider the following integral transform of a function g(t) with kernel h(t, z), F(z) := 1 0 h(t, z)g(t)dt. We require for the function h(t, z) to be uniformly bounded for z ∈D⊂ C by a function H(t) integrable in t ∈ [0, 1], and for the function g(t) to be analytic in an open region Ω that contains the open interval (0, 1). Then, we derive expansions of F(z) in terms of the moments of the function h, M[h(·, z), n] := 1 0 h(t, z)tndt, that are uniformly convergent for z ∈ D. The convergence of the expansion is of exponential order O(a−n), a > 1, when [0, 1] ∈ Ω and of power order O(n−b), b > 0, when [0, 1] ∈/ Ω. Most of the special functions F(z) having an integral representation may be cast in this form, possibly after an appropriate change of the integration variable. Then, special interest has the case when the moments M[h(·, z), n] are elementary functions of z, because in that case the uniformly convergent expansion derived for F(z) is given in terms of elementary functions. We illustrate the theory with several examples of special functions different from those considered in [Bujanda & all, 2018-2019].Show more Publication Open Access A note on the asymptotic expansion of the Lerch’s transcendent(Taylor & Francis, 2018) Cai, Xing Shi; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika IngeniaritzaShow more In Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], the authors derived an asymptotic expansion of the Lerch's transcendent Φ(z,s,a) for large |a|, valid for Ra>0, Rs>0 and z∈C∖[1,∞). In this paper, we study the special case z≥1 not covered in Ferreira and López [Asymptotic expansions of the Hurwitz–Lerch zeta function. J Math Anal Appl. 2004;298(1):210–224], deriving a complete asymptotic expansion of the Lerch's transcendent Φ(z,s,a) for z>1 and Rs>0 as Ra goes to infinity. We also show that when a is a positive integer, this expansion is convergent for Rz≥1. As a corollary, we get a full asymptotic expansion for the sum ∑mn=1zn/ns for fixed z>1 as m→∞. Some numerical results show the accuracy of the approximation.Show more Publication Open Access New series expansions for the ℋ-function of communication theory(Taylor & Francis, 2023) Ferreira, Chelo; López García, José Luis; Pérez Sinusía, Ester; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more 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 paper we investigate several convergentand/or asymptotic expansions ofHp(z,b,η)for some limiting valuesof their variables and parameters: large values ofz, large values ofp, small values ofη, and values ofb→1. We provide explicit and/orrecursive algorithms for the computation of the coefficients of theexpansions. Some numerical examples illustrate the accuracy of theapproximations.Show more Publication Open Access A convergent and asymptotic Laplace method for integrals(Elsevier, 2023) López García, José Luis; Pagola Martínez, Pedro Jesús; Palacios Herrero, Pablo; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas; Universidad Pública de Navarra / Nafarroako Unibertsitate PublikoaShow more 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 special functions that have a Laplace integral representation. But in most of the important examples of special functions, the asymptotic expansion derived by means of Watson’s lemma or Laplace’s method is not convergent. A modification of Watson’s lemma was introduced in [Nielsen, 1906] where, by the use of inverse factorial series, a new asymptotic as well as convergent expansion of F (z), for the particular case f (t) = t, was derived. In this paper we go some steps further and investigate a modification of the Laplace’s method for F (z), with a general phase function f (t), to derive asymptotic expansions of F (z) that are also convergent, accompanied by error bounds. An analysis of the remainder of this new expansion shows that it is convergent under a mild condition for the functions f (t) and g(t), namely, these functions must be analytic in certain starlike complex regions that contain the positive axis [0,∞). In many practical situations (in many examples of special functions), the singularities of f (t) and g(t) are off this region and then this method provides asymptotic expansions that are also convergent. We illustrate this modification of the Laplace’s method with the parabolic cylinder function U(a, z), providing an asymptotic expansions of this function for large z that is also convergent.Show more