Dirichlet Averages of Wright-Type Hypergeometric Function

Farooq Ahmad; D. K. Jain; Alok Jain; Altaf Ahmad

doi:doi:10.11648/j.dmath.20170201.12

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Dirichlet Averages of Wright-Type Hypergeometric Function

Farooq Ahmad, D. K. Jain, Alok Jain, Altaf Ahmad

Published in International Journal of Discrete Mathematics (Volume 2, Issue 1)

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.

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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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TY  - JOUR
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
PY  - 2017
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
SP  - 6
EP  - 9
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

Farooq Ahmad

Department of Mathematics, Govt. Degree College Kupwara (J&K), India
D. K. Jain

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

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

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

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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}
}

Copy | Download

TY  - JOUR
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
PY  - 2017
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
SP  - 6
EP  - 9
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  -

Copy | Download