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Dirichlet Averages of Wright-Type Hypergeometric Function

Received: 23 December 2016     Accepted: 21 January 2017     Published: 20 February 2017
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Abstract

In the present paper, the authors approach is based on the use of Dirichlet averages of the generalized Wright-type hyper geometric function introduced by Wright in like the functions of the Mittag-Leffler type, the functions of the Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly due to the fact that they are interrelated with the Mittag-Leffler functions through Laplace and Fourier transformations.

Published in International Journal of Discrete Mathematics (Volume 2, Issue 1)
DOI 10.11648/j.dmath.20170201.12
Page(s) 6-9
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Dirichlet Averages, Reimann-Liouville Fractional Integral, Wright Type Hyper Geometric Function

References
[1] Carlson. B. C, (1963), Lauricella’shypergeometric function FD, J. Math. Anal. Appl. 7, 452-470.
[2] Carlson. B. C. (1969), A connection between elementary and higher transcendental functions, SIAM J. Appl. Math. 17, No. 1, 116-148.
[3] Carlson. B. C. (1991), B-splines, hypergeometric functions and Dirichlets average, J. Approx. Theory 67, 311-325.
[4] Castell. W. zu. (2002), Dirichlet splines as fractional integrals of B-splines, Rocky Mountain J. Math. 32, No. 2, pp. 545-559.
[5] Massopust. P, Forster. B (2010), Multivariate complex B-splines and Dirichlet averages, J. Approx. Theory 162, No. 2, 252-269.
[6] Andrews. G. E, Askey. R, Roy. R (1999), Special Functions, Cambridge University Press.
[7] Carlson. B. C. (1977), Special Functions of Applied Mathematics, Academic Press, New York.
[8] Banerji. P. K, lecture notes on generalized integration and differentiation and Dirichlet averages.
[9] Capelas de Oliveira. E, F. Mainardi and J. VazJr (2011), Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics European Journal of Physics, Special Topics, Vol. 193.
[10] Al. Salam, W. A (1966), Some fractional q- integral and q- derivatives. Proc. Edin. Math. Soc.17, 616-621.
[11] Dotsenko, M.” On some applications of Wright type hypergeometric function’’ Comptes Rendus de l’Academie Bulgare des Sciences, Vol. 44, 1991, pp, 13-16.
[12] Virchenko, N. Kalla S. L. and Al-Zamel A. “Some Results on generalized Hypergeometric functions,” Integral Transforms and Special functions, Vol. 12, no1, 2001, pp. 89-100.
Cite This Article
  • APA Style

    Farooq Ahmad, D. K. Jain, Alok Jain, Altaf Ahmad. (2017). Dirichlet Averages of Wright-Type Hypergeometric Function. International Journal of Discrete Mathematics, 2(1), 6-9. https://doi.org/10.11648/j.dmath.20170201.12

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    ACS Style

    Farooq Ahmad; D. K. Jain; Alok Jain; Altaf Ahmad. Dirichlet Averages of Wright-Type Hypergeometric Function. Int. J. Discrete Math. 2017, 2(1), 6-9. doi: 10.11648/j.dmath.20170201.12

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    AMA Style

    Farooq Ahmad, D. K. Jain, Alok Jain, Altaf Ahmad. Dirichlet Averages of Wright-Type Hypergeometric Function. Int J Discrete Math. 2017;2(1):6-9. doi: 10.11648/j.dmath.20170201.12

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  • @article{10.11648/j.dmath.20170201.12,
      author = {Farooq Ahmad and D. K. Jain and Alok Jain and Altaf Ahmad},
      title = {Dirichlet Averages of Wright-Type Hypergeometric Function},
      journal = {International Journal of Discrete Mathematics},
      volume = {2},
      number = {1},
      pages = {6-9},
      doi = {10.11648/j.dmath.20170201.12},
      url = {https://doi.org/10.11648/j.dmath.20170201.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.dmath.20170201.12},
      abstract = {In the present paper, the authors approach is based on the use of Dirichlet averages of the generalized Wright-type hyper geometric function introduced by Wright in like the functions of the Mittag-Leffler type, the functions of the Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly due to the fact that they are interrelated with the Mittag-Leffler functions through Laplace and Fourier transformations.},
     year = {2017}
    }
    

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    T1  - Dirichlet Averages of Wright-Type Hypergeometric Function
    AU  - Farooq Ahmad
    AU  - D. K. Jain
    AU  - Alok Jain
    AU  - Altaf Ahmad
    Y1  - 2017/02/20
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    N1  - https://doi.org/10.11648/j.dmath.20170201.12
    DO  - 10.11648/j.dmath.20170201.12
    T2  - International Journal of Discrete Mathematics
    JF  - International Journal of Discrete Mathematics
    JO  - International Journal of Discrete Mathematics
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    PB  - Science Publishing Group
    SN  - 2578-9252
    UR  - https://doi.org/10.11648/j.dmath.20170201.12
    AB  - In the present paper, the authors approach is based on the use of Dirichlet averages of the generalized Wright-type hyper geometric function introduced by Wright in like the functions of the Mittag-Leffler type, the functions of the Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly due to the fact that they are interrelated with the Mittag-Leffler functions through Laplace and Fourier transformations.
    VL  - 2
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Govt. Degree College Kupwara (J&K), India

  • Department of Applied Mathematics, Madhav Institute of Technology & Science, Gwalior (M. P.), India

  • School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, (M. P.), India

  • School of Mathematics and Allied Sciences, Jiwaji University, Gwalior, (M. P.), India

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