Properties and Applications of Extended Hypergeometric Functions

Authors

DOI:

https://doi.org/10.17230/ingciencia.10.19.1

Keywords:

beta distribution, extended beta function, extended confluent hyper- geometric function, extended gamma function, extended Gauss hypergeometric function, gamma distribution, quotient, Gauss hypergeometric function

Abstract

In this article, we study several properties of extended Gauss hypergeometric and extended confluent hypergeometric functions. We derive several integrals, inequalities and establish relationship between these and other special functions. We also show that these functions occur naturally in statistical distribution theory.

MSC: 33C90

Downloads

Download data is not yet available.

Author Biographies

  • Daya Krishna Nagar, Universidad de Antioquia

    Ph.D. in Science, profesor titular, Departamento de Matemáticas, Universidad de Antioquia, Medellín, Colombia.

  • Raúl Alejandro Morán-Vásquez, Universidade de São Paulo

    MSc. in Matemáthics

  • Arjun K Gupta, Bowling Green State University
    PhD. in Statistics

References

Y. L. Luke, The special functions and their approximations, Vol. I, ser. Mathematics in Science and Engineering, Vol. 53. New York: Academic Press, 1969. 12

M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, “Extension of Euler’s beta function,” J. Comput. Appl. Math., vol. 78, no. 1, pp. 19–32, 1997. [Online]. Available: http://dx.doi.org/10.1016/S0377-0427(96)00102-1 13, 15, 25

A. R. Miller, “Remarks on a generalized beta function,” J. Comput. Appl. Math., vol. 100, no. 1, pp. 23–32, 1998. [Online]. Available: http://dx.doi.org/10.1016/S0377-0427(98)00121-6 13, 14, 18

M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, “Extended hypergeometric and confluent hypergeometric functions,” Appl. Math. Comput., vol. 159, no. 2, pp. 589–602, 2004. [Online]. Available: http://dx.doi.org/10.1016/j.amc.2003.09.017 13, 14, 15

I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and products, 7th ed. Elsevier/Academic Press, Amsterdam, 2007, translated from the Russian, Translation edited and with a preface by Alan Jeffrey and Daniel Zwillinger, With one CD-ROM (Windows, Macintosh and UNIX). 15

N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous univariate distributions. Vol. 2, 2nd ed., ser. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. New York: John Wiley & Sons Inc., 1995, a Wiley-Interscience Publication. 24

A. K. Gupta and D. K. Nagar, Matrix variate distributions, ser. Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics. Chapman & Hall/CRC, Boca Raton, FL, 2000, vol. 104. 24

D. K. Nagar and E. Zarrazola, “Distributions of the product and the quotient of independent Kummer-beta variables,” Sci. Math. Jpn., vol. 61, no. 1, pp. 109–117, 2005. [Online]. Available: http://www.jams.or.jp/scm/contents/e-2004-1/2004-4.pdf 29

R. A. Morán-Vásquez and D. K. Nagar, “Product and quotients of independent Kummer-gamma variables,” Far East J. Theor. Stat., vol. 27, no. 1, pp.41–55, 2009. 29

J. A. Castillo Pérez and C. Jiménez Ruiz, “Algunas representaciones simples de la función hipergeométrica generalizada 2r1(a; b; c; _ ; x),” Ingeniería y Ciencia, vol. 2, no. 4, pp. 75–94, 2006. [Online]. Available: http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/464 30

J. A. Castillo Pérez, “Algunas integrales impropias con límites de integración infinitos que involucran a la generalización _ de la función hipergeométrica de gauss,” Ingeniería y Ciencia, vol. 3, no. 5, pp. 67–85, 2007. [Online]. Available: http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/456 30

——, “Algunas integrales que involucran a la función hipergeométrica generalizada,” Ingeniería y Ciencia, vol. 4, no. 7, pp. 7–22, 2008. [Online]. Available: http://publicaciones.eafit.edu.co/index.php/ingciencia/ article/view/224 30

J. A. Castillo Pérez and L. Galué, “Algunas integrales indefinidas que contienen a la función hipergeométrica generalizada,” Ingeniería y Ciencia, vol. 5, no. 9, pp. 45–54, 2009. [Online]. Available: http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/467 30

Downloads

Published

2014-01-31

Issue

Vol. 10 No. 19 (2014)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

 

How to Cite

Nagar, D. K., Morán-Vásquez, R. A., & Gupta, A. K. (2014). Properties and Applications of Extended Hypergeometric Functions. Ingeniería Y Ciencia, 10(19), 11-31. https://doi.org/10.17230/ingciencia.10.19.1

Most read articles by the same author(s)