Generalized q-Mittag-Leffler function and its properties.

• Nathwani, B. V. ^[1]
  1. [1] Maharaja Sayajirao University of Baroda

     Maharaja Sayajirao University of Baroda

     India

     
• Localización: Divulgaciones matemáticas, ISSN-e 1315-2068, Vol. 18, Nº. 1, 2017 (Ejemplar dedicado a: Divulgaciones Matemáticas), págs. 10-33
• Idioma: español
• Enlaces
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• Resumen

  • Motivated essentially by the success of the applications of the Mittag-Leffler functions in Science and Engineering, we propose here a unification of certain q-extensions of generalizations of Mittag-Leffler function together with Saxena-Nishimoto's function, Bessel-Maitland function, Dotsenko function, Elliptic Function, etc. We obtain Mellin-Barnes contour integral representation, a q-difference equation, Eigen function property. As a specialization, a generalization of q-Konhauser polynomial is considered for which the series inequality relations and inverse series relations are obtained.-----------------------------------------------------------------------------Motivados esencialmente por el éxito de las aplicaciones de las funciones de Mittag-Leffler en Ciencia e Ingeniería, proponemos aquí una unificación de ciertas q-extensiones de generalizaciones de la función de Mittag-Leffler incluyendo la función de Saxena-Nishimoto, la función de Bessel-Maitland, función de Dotsenko, función elíptica, etc. Obtenemos la representación integral de contorno de Mellin-Barnes, una ecuación de q-diferencia, propiedad de función Eigen. Como especialización, se considera un polinomio generalizado de q-Konhauser para el cual se obtienen las relaciones de desigualdad en serie y relaciones en serie inversa.

• Referencias bibliográficas
  • W. A. Al-Salam and A. Verma. q-Konhauser polynomials, Pacific Journal of Mathematics 1(108) (1983), 1-7.
  • M. H. Annaby and Z. S. Mansour. q-Fractional calculus and equations, Springer-Verlag Berlin Heidelberg (2012).
  • B. I. Dave and M. Dalbide. Gessel-Stanton's inverse series and a system of q-polynomials.
  • Bull. Sci. Math. 138 (2014), 323-334.
  • G. Gasper and M. Rahman. Basic Hypergeometric Series. Cambridge University Press, Cambridge (1990).
  • I. S. Gupta and L. Debnath. Some properties of the Mittag-Leffler functions. Integral Trans.
  • Spec. Funct. 18(5) (2007), 329-336.
  • H. J. Haubold, A. M. Mathai, and R. K. Saxena. The $H$-Function: Theory and Applications},
  • Centre for Mathematical Sciences, Pala Campus, Kerala, India {bf 37} (2008).
  • A. A. Kilbas, M. Saigo, and R. K. Saxena. Generalized Mittag-Leffler function and generalized fractional calculus operators. Integral Transforms...
  • V. S. Kiryakova. Multiple (multiindex) Mittag-Leffler functions and relations to generalized
  • fractional calculus. Journal of Computational and Applied Mathematics 118 (2000), 241-259.
  • Y. L. Luke. The Special Functions and their approximations. Academic Press, New York,
  • M. Mansour. An asymptotic expansion of the q-Gamma function. Journal of Nonlinear Mathematical Physics 13(4) (2006), 479-483.
  • G. Mittag-Leffler. Sur la nouvelle fonction. C. R. Acad. Sci., Paris 137 (1903), 554-558.
  • S.D. Purohit and S.L. Kalla. A generalization of q-Mittag-Leffler function. Mat.Bilt., 35 (2011), 15-26.
  • J. Riordan. Combinatorial identities. Wiley, New York/London/Sydney (1968).
  • M. Saigo and A. A. Kilbas. On Mittag Leffler type function and applications. Integral Transforms Spec. Funct., 7 (1998), 97-112.
  • R. K. Saxena, S. Kalla, and R. Saxena. Multivariate analogue of generatized Mittag-Leffer function. Integral Transform. Spec. Funct., 22(7)...
  • R. K. Saxena and K. N. Nishimoto. Fractional calculus of generalized Mittag-Leffler functions. J. Fract. Calc., 37 (2010), 43-52.
  • A. K. Shukla and J. C. Prajapati. On a generalization of Mittag-Leffler function and its properties. J. Math. Anal. Appl., 336(2) (2007),...
  • A. Wiman. Über de fundamental satz in der theoric der funktionen, Acta Math. 29 (1905), 191-201.