Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Some properties of a family of incomplete hypergeometric functions

  • Published:
Russian Journal of Mathematical Physics Aims and scope Submit manuscript

Abstract

Recently, Srivastava et al. introduced and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Our principal objective in this paper is to investigate several further properties of these incomplete hypergeometric functions and some general classes of incomplete hypergeometric polynomials associated with them. Various (known or new) special cases and consequences of the results presented in this paper are also considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Abramowitz and I. A. Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Tenth Printing (National Bureau of Standards, Applied Mathematics Series 55, National Bureau of Standards, Washington, D.C., 1972; Reprinted by Dover Publications, New York, 1965) (see also [17] below).

    MATH  Google Scholar 

  2. L. C. Andrews, Special Functions for Engineers and Applied Mathematicians (Macmillan Company, New York, 1984).

    Google Scholar 

  3. W. N. Bailey, Generalized Hypergeometric Series, Cambridge Tracts in Mathematics and Mathematical Physics, 32 (Cambridge University Press, Cambridge, London-New York, 1935; Reprinted by Stechert-Hafner Service Agency, New York and London, 1964).

    MATH  Google Scholar 

  4. F. Brafman, “Some Generating Functions for Laguerre and Hermite polynomials,” Canad. J. Math. 9, 180–187 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  5. B. C. Carlson, Special Functions of Applied Mathematics (Academic Press, New York, San Francisco and London, 1977).

    MATH  Google Scholar 

  6. M. A. Chaudhry and S. M. Zubair, On a Class of Incomplete Gamma Functions with Applications (Chapman and Hall (CRC Press Company), Boca Raton, London, New York and Washington, D.C., 2001).

    Book  Google Scholar 

  7. T. W. Chaundy, “An Extension of Hypergeometric Functions, I,” (I), Q. J. Math. 14, 55–78 (1943).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. A. Erdélyi, W. Mangus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, I (McGraw-Hill Book Company, New York, Toronto and London, 1953).

    Google Scholar 

  9. A. Erdélyi, W. Mangus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, III (McGraw-Hill Book Company, New York, Toronto and London, 1955).

    MATH  Google Scholar 

  10. N. L. Johnson, S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, 2 (John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1995).

    MATH  Google Scholar 

  11. P. W. Karlsson, “Hypergeometric Functions with Integral Parameter Differences,” J. Mathematical Phys. 12(2), 270–271 (1971).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematical Studies, 204 (Elsevier (North-Holland) Science Publishers, Amsterdam, London and New York, 2006).

    Book  MATH  Google Scholar 

  13. Y. L. Luke, Mathematical Functions and Their Approximations (Academic Press, New York, San Francisco and London, 1975).

    MATH  Google Scholar 

  14. W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics, Third Enlarged ed., Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtingung der Anwendungsgebiete, Band 52 (Springer-Verlag, Berlin, Heidelberg and New York, 1966).

    MATH  Google Scholar 

  15. A. R. Miller and H. M. Srivastava, “Karlsson-Minton Summation Theorems for the Generalized Hyppergeometric Series of Unit Argument,” Integral Transforms Spec. Funct. 21(7–8), 603–612 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  16. K. B. Oldham, J. Myland, and J. Spanier, An Atlas of Functions. With Equator, the Atlas Function Calculator, Second edition [With 1 CD-ROM (Windows)] (Springer, Berlin, Heidelberg and New York, 2009).

    Book  Google Scholar 

  17. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (Eds.), NIST Handbook of Mathematical Functions [With 1 CD-ROM (Windows, Macintosh and UNIX)] (U. S. Department of Commerce, National Institute of Standards and Technology, Washington, D. C., 2010; Cambridge University Press, Cambridge, London and New York, 2010) (see also [1] above).

    MATH  Google Scholar 

  18. R. Panda, “A Note on Certain Reducible Cases of the Generalized Hypergeometric Function,” Indag. Math. 38(1), 41–45 (1976).

    MathSciNet  Google Scholar 

  19. R. Panda, “The Reducible Cases of Certain Generalized Hypergeometric Functions of Several Variables,” Indag. Math. 39(5), 469–476 (1977).

    MathSciNet  Google Scholar 

  20. E. D. Rainville, Special Functions (Macmillan Company, New York, 1960; Reprinted by Chelsea publishing Company, Bronx, New York, 1971).

    MATH  Google Scholar 

  21. L. J. Slater, Generalized Hypergeometric Functions (Cambridge University Press, Cambridge, London and New York, 1966).

    MATH  Google Scholar 

  22. H. M. Srivastava, “Generalized Hypergeometric Functions with Integral Parameter Differences,” Indag. Indag. Math. 35, 38–40 (1973).

    Article  Google Scholar 

  23. H. M. Srivastava, “A Family of q-Generating Functions,” Bull. Inst. Math. Acad. Sinica 12(4), 327–336 (1984).

    MathSciNet  MATH  Google Scholar 

  24. H. M. Srivastava, M. A. Chaudhry, and R. P. Agarwal, “The Incomplete Pochhammer Symbols and Their Applications to Hypergeometric and Related Functions,” Integral Transforms Spec. Funct. 23(9), 659–683 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  25. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions (Kluwer Acedemic Publishers, Dordrecht, Boston and London, 2001).

    Book  MATH  Google Scholar 

  26. H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals (Elsevier Science Publishers, Amsterdam, London and New York, 2012).

    MATH  Google Scholar 

  27. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series (Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985).

    MATH  Google Scholar 

  28. H. M. Srivastava and B. R. K. Kashyap, Special Functions in Queuing Theory and Related Stochastic Processes (Academic Press, New York and London, 1982).

    MATH  Google Scholar 

  29. H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions (Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984).

    MATH  Google Scholar 

  30. R. Srivastava, “Some Families of Combinatorial and Other Series Identities and Their Applications,” Appl. Math. Comput. 218(3), 1077–1083 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  31. N. M. Temme, Special Functions: An Introduction to Classical Functions of Mathematical Physics (A Wiley-Interscience Publication, John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1996).

    Book  MATH  Google Scholar 

  32. G. N. Watson, A Treatise on the Theory of Bessel Functions, Second ed. (Cambridge University Press, Cambridge, London and New York, 1944).

    MATH  Google Scholar 

  33. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes and of Analytic Functions; with an Account of the Principal Transcendental Functions, Fourth Ed. (Reprinted) (Cambridge University Press, Cambridge, London and New York, 1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria Victoria, British, Columbia, V8W 3R4, Canada

    R. Srivastava

Authors
  1. R. Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Srivastava.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Srivastava, R. Some properties of a family of incomplete hypergeometric functions. Russ. J. Math. Phys. 20, 121–128 (2013). https://doi.org/10.1134/S1061920813010111

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1061920813010111

Keywords

Search

Navigation