Now showing items 1-14 of 14

    • Analytic formulas for the evaluation of the Pearcey integral 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (American Mathematical Society, 2017)   Artículo / Artikulua  OpenAccess
      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 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      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 ...
    • Convergent and asymptotic expansions of the Pearcey integral 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (Elsevier, 2015)   Artículo / Artikulua  OpenAccess
      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 ...
    • Convergent expansions of the Bessel functions in terms of elementary functions 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (Springer US, 2018)   Artículo / Artikulua  OpenAccess
      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 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (American Mathematical Society, 2018)   Artículo / Artikulua  OpenAccess
      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 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (World Scientific Publishing, 2017)   Artículo / Artikulua  OpenAccess
      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 ...
    • New analytic representations of the hypergeometric functions p+1Fp 

      López García, José Luis Upna Orcid; Palacios Herrero, Pablo Upna Orcid; Pagola Martínez, Pedro Jesús Upna (Springer, 2021)   Artículo / Artikulua  OpenAccess
      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 ...
    • New asymptotic expansion and error bound for Stirling formula of reciprocal Gamma function 

      Pagola Martínez, Pedro Jesús Upna (Ele-Math, 2018)   Artículo / Artikulua  OpenAccess
      Studying the problem about if certain probability measures are determinate by its moments [4, 8, 10] is useful to know the asymptotic behavior of the probability densities for large values of argument. This requires, ...
    • New series expansions of the 3F2 function 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Pérez Sinusía, Ester Upna Orcid (2015)   Artículo / Artikulua  OpenAccess
      We can use the power series definition of 3F2(a1, a2, a3; b1, b2; z) to compute this function for z in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. ...
    • The Pearcey integral in the highly oscillatory region 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna (Elsevier, 2016)   Artículo / Artikulua  OpenAccess
      We consider the Pearcey integral P(x, y) for large values of |y| and bounded values of |x|. The integrand of the Pearcey integral oscillates wildly in this region and the asymptotic saddle point analysis is complicated. ...
    • Series representations of the Volterra function and the Fransén–Robinson constant 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Elsevier, 2021)   Artículo / Artikulua
      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 ...
    • Uniform approximations of the first symmetric elliptic integral in terms of elementary functions 

      Bujanda Cirauqui, Blanca Upna Orcid; López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Palacios Herrero, Pablo Upna Orcid (Springer, 2022)   Artículo / Artikulua  OpenAccess
      We 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 ...
    • Uniform convergent expansions of integral transforms 

      López García, José Luis Upna Orcid; Palacios Herrero, Pablo Upna Orcid; Pagola Martínez, Pedro Jesús Upna (American Mathematical Society, 2021)   Artículo / Artikulua  OpenAccess
      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 ...
    • Uniformly convergent expansions for the generalized hypergeometric functions p –1Fp and pFp 

      López García, José Luis Upna Orcid; Pagola Martínez, Pedro Jesús Upna; Karp, D. B. (Taylor & Francis, 2020)   Artículo / Artikulua  OpenAccess
      We 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 ...