López García, José Luis

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https://academica-e.unavarra.es/handle/2454/49435

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López García

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José Luis

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Estadística, Informática y Matemáticas

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InaMat2. Instituto de Investigación en Materiales Avanzados y Matemáticas

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0000-0002-6050-9015

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88571

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2369

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2017 - 20183
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End date: 2019 × Subject: Generalized hypergeometric function ×

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Now showing 1 - 3 of 3
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    PublicationOpen Access
    On a particular class of Meijer's G functions appearing in fractional calculus
    (Academic Publications, 2018) Karp, D. B.; López García, José Luis; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
    In this paper we investigate the Meijer G-function G p+1,p+1 p,1 which, for certain parameter values, represents the Riemann-Liouville fractional integral of the Meijer-Nørlund function G p,p. p,0 The properties of this function play an important role in extending the multiple Erdélyi-Kober fractional integral operator to arbitrary values of the parameters which is investigated in a separate work, in Fract. Calc. Appl. Anal., Vol. 21, No 5 (2018). Our results for G p+1,p+1 p,1 include: a regularization formula for overlapping poles, a connection formula with the Meijer-Nørlund function, asymptotic formulas around the origin and unity, formulas for the moments, a hypergeometric transform and a sign stabilization theorem for growing parameters.
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    PublicationOpen Access
    An extension of the multiple Erdélyi-Kober operator and representations of the generalized hypergeometric functions
    (De Gruyter, 2018) Karp, D. B.; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
    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 derivatives of the function in question and the integration with respect to a kernel expressed in terms of special case of Meijer's G function. An action of the regularized multiple Erd elyi-Kober operator on some simple kernels leads to decomposition formulas for the generalized hypergeometric functions. In the ultimate section, we de ne an alternative regularization better suited for representing the Bessel type generalized hypergeometric function p􀀀1Fp. A particular case of this regularization is then used to identify some new facts about the positivity and reality of zeros of this function.
  • Thumbnail Image
    PublicationOpen Access
    Representations of hypergeometric functions for arbitrary parameter values and their use
    (2017) Karp, D. B.; López García, José Luis; Ingeniería Matemática e Informática; Matematika eta Informatika Ingeniaritza
    Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and show that the extended representations can be interpreted as examples of regularizations of integrals containing Meijer's G function. Second, we give new applications of both, known and extended representations. These include: inverse factorial series expansion for the Gauss type function, new information about zeros of the Bessel and Kummer type functions, connection with radial positive de nite functions and generalizations of Luke's inequalities for the Kummer and Gauss type functions.