Mediterranean Journal of Mathematics

, Volume 10, Issue 4, pp 1853–1865 | Cite as

The Second Appell Function for one Large Variable

  • Chelo Ferreira
  • José L. López
  • Ester Pérez Sinusía


We consider the Mellin convolution integral representation of the second Appell function given in [8]. Then, we apply the asymptotic method designed in [12] for this kind of integrals to derive new asymptotic expansions of the Appell function F 2 for one large variable in terms of hypergeometric functions. For certain values of the parameters, some of these expansions involve logarithmic terms in the asymptotic variables. The accuracy of the approximations is illustrated with numerical experiments.

Mathematics Subject Classification (2010)

41A60 33C65 


Second Appell hypergeometric function asymptotic expansions Mellin convolution integrals 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Chelo Ferreira
    • 1
  • José L. López
    • 2
  • Ester Pérez Sinusía
    • 3
  1. 1.Dpto. de Matemática Aplicada, IUMAUniversidad de ZaragozaZaragozaSpain
  2. 2.Dpto. de Ingeniería Matemática e InformáticaUniversidad Pública de NavarraPamplonaSpain
  3. 3.Dpto. de Matemática Aplicada, IUMAUniversidad de ZaragozaZaragozaSpain

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