Person: López García, José Luis
Loading...
Email Address
person.page.identifierURI
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
8 results
Search Results
Now showing 1 - 8 of 8
Publication Open Access An analytic representation of the second symmetric standard elliptic integral in terms of elementary functions(Springer, 2022) Bujanda Cirauqui, Blanca; 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 PublikoaWe 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 variables x, y or z (with the other two fixed). We proceed by considering a more general parametric integral from which RD(x,y,z) is a particular case. It turns out that this parametric integral is an integral representation of the Appell function F1(a;b,c;a+1;x,y). Therefore, as a byproduct, we deduce convergent expansions of F1(a;b,c;a+1;x,y). We also compute error bounds at any order of the approximation. Some numerical examples show the accuracy of the expansions and their uniform features.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 PublikoaA 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.Publication Open Access Uniform approximations of the first symmetric elliptic integral in terms of elementary functions(Springer, 2022) Bujanda Cirauqui, Blanca; 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; Gobierno de Navarra / Nafarroako GobernuaWe 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 or z in closed subsets (possibly unbounded) of C\ (−∞, 0]. The expansions are accompanied by error bounds. The accuracy of the expansions and their uniform features are illustrated by means of some numerical examples.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 PublikoaSeveral 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].Publication Open Access Uniform convergent expansions of the error function in terms of elementary functions(Springer, 2023) Ferreira González, 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 PublikoaWe 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) | <π/4. The expansion is accompanied by realistic error bounds.Publication Open Access Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp(Taylor & Francis, 2020) López García, José Luis; Pagola Martínez, Pedro Jesús; Karp, D. B.; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y MatemáticasWe 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 further obtain a convergent expansion of the generalized hypergeometric function p F p in terms of the confluent hypergeometric functions 1 F 1 that holds uniformly in any right half-plane. For both functions, we make a further step forward and give convergent expansions in terms of trigonometric, exponential and rational functions that hold uniformly in the same domains. For all four expansions we present explicit error bounds. The accuracy of the approximations is illustrated by some numerical experiments.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 PublikoaTheH-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.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 PublikoaWatson’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.