Two Classes of Integrals Involving Extended Wright Type Generalized Hypergeometric Function

Authors

  • A. Ghaffar Department of Mathematical Sciences, BUITEMS Quetta
  • A. Saif Department of Mathematical Sciences, BUITEMS Quetta
  • M. Iqbal Department of Mathematical Sciences, BUITEMS Quetta
  • M. Rizwan Department of General Studies, Jubail Industrial College, Jubail, Kingdom of Saudi Arabia

DOI:

https://doi.org/10.26713/cma.v10i3.1190

Keywords:

Wright type hypergeometric function, Wright type generalized hypergeometric function, hypergeometric function, generalized hypergeometric function

Abstract

In this article, our main purpose is to investigate generalized integral formulas containing the extended Wright type generalized hypergeometric function. Moreover, certain special cases of the main results given here have also been pointed out for the Wright type hypergeometric function.

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References

S. Araci, G. Rahman, A. Ghaffar and K. S. Nisar, Fractional calculus of extended Mittag-Leffler function and its applications to statistical distribution, Mathematics 7(3) (2019), 248, DOI: 10.3390/math7030248.

M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with applications, Journal of Computational and Applied Mathematics 55(1) (1994), 99 – 123, DOI: 10.1016/0377-0427(94)90187-2.

M. A. Chaudhry and S. M. Zubair, On the decomposition of generalized incomplete gamma functions with applications to Fourier transforms, Journal of Computational and Applied Mathematics 59(3) (1995), 253 – 284, DOI: 10.1016/0377-0427(94)00026-W.

M. A. Chaudhry and S. M. Zubair, Extended incomplete gamma functions with applications, Journal of Mathematical Analysis and Applications 274(2) (2002), 725 – 745, DOI: 10.1016/S0022-247X(02)00354-2.

M. A. Chaudhry, A. Qadir, M. Rafique and S. M. Zubair, Extension of Euler's beta function, Journal of Computational and Applied Mathematics 78(1) (1997), 19 – 32, DOI: 10.1016/S0377-0427(96)00102-1.

M. A. Chaudhry, A. Qadir, H. M. Srivastava and R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Applied Mathematics and Computation 159(2) (2004), 589 – 602, DOI: 10.1016/j.amc.2003.09.017.

M. A. Chaudhry, N. M. Temme and E. J. M. Veling, Asymptotics and closed form of a generalized incomplete gamma function, Journal of Computational and Applied Mathematics 67(2) (1996), 371 – 379, DOI: 10.1016/0377-0427(95)00018-6.

M. R. Dotsenko, On some applications of Wrights hypergeometric function, Dokladi Na Bolgarskata Akademiya Na Naukite 44(6) (1991), 13 – 16.

M. Dotsenko, On some applications of Wright's hypergeometric function, Comptes Rendus de l'Academie Bulgare des Sciences 44 (1991), 13 – 16.

A. Erdelyi, W. Magnus, F. Oberhettinger, F. G. Tricomi and H. Bateman, Higher Transcendental Functions, Vol. 1, p. 31, McGraw-Hill, New York (1953), https://authors.library.caltech.edu/43491/1/Volume%201.pdf.

J. L. Lavoie and G. Trottier, On the sum of certain Appells series, Ganita 201 (1969), 31 – 32.

V. Malovichko, On a generalized hypergeometric function and some integral operators, Math. Phys. 19 (1976), 99 – 103.

F. Oberhettinger, Tables of Mellin Transforms, Springer Science & Business Media (2012), DOI: 10.1007/978-3-642-65975-1.

G. Rahman, A. Ghaffar, K. S. Nisar adn A. Azeema, The ((k,s))-fractional calculus of class of a function, Honam Mathematical J. 40(1) (2018), 125 – 138, DOI: 10.5831/HMJ.2018.40.1.125.

G. Rahman, A. Ghaffar, K. S. Nisar adn S. Mubeen, A new class of integrals involving extended Mittag-Leffler functions, Journal of Fractional Calculus and Applications 8(20) (2017), 56 – 61, DOI: 10.20944/preprints201705.0222.v1.

G. Rahman, A. Ghaffar, S. Mubeen, M. Arshad and S. U. Khan, The composition of extended Mittag-Leffler functions with pathway integral operator, Advances in Difference Equations 2017(1) (2017), 176, DOI: 10.1186/s13662-017-1237-8.

E. M. Wright, On the coefficients of power series having exponential singularities, Journal of the London Mathematical Society 1(1) (1933), 71 – 79, DOI: 10.1112/jlms/s1-8.1.71.

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Published

30-09-2019
CITATION

How to Cite

Ghaffar, A., Saif, A., Iqbal, M., & Rizwan, M. (2019). Two Classes of Integrals Involving Extended Wright Type Generalized Hypergeometric Function. Communications in Mathematics and Applications, 10(3), 599–606. https://doi.org/10.26713/cma.v10i3.1190

Issue

Vol. 10 No. 3 (2019)

Section

Research Article

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