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SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION
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 Title & Authors
SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION
Rao, Snehal B.; Patel, Amit D.; Prajapati, Jyotindra C.; Shukla, Ajay K.;
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 Abstract
In present paper, we obtain functions and by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function and some special cases have also been discussed.
 Keywords
generalized hypergeometric function;recurrence relation;integral representation;fractional integral and differential operators;
 Language
English
 Cited by
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2.
Some properties of Wright-type generalized hypergeometric function via fractional calculus, Advances in Difference Equations, 2014, 2014, 1, 119  crossref(new windwow)
 References
1.
L. Debnath and D. Bhatta, Integral Transforms and Their Applications, Chapman and Hall/CRC press, Boca Raton, FL, 2007.

2.
M. Dotsenko, On some applications of Wright's hypergeometric function, C. R. Acad. Bulgare Sci. 44 (1991), no. 6, 13-16.

3.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vols. I, II, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953.

4.
A. A. Kilbas and M. Saigo, H-Transforms, Chapman and Hall/CRC press, Boca Raton, FL, 2004

5.
A. A. Kilbas, M. Saigo, and J. J. Trujillo, On the generalized Wright function, Fract. Calc. Appl. Anal. 5 (2002), no. 4, 437-460.

6.
V. Kiryakova, Generalized Fractional Calculus and Applications, Wiley & Sons. Inc., New York, 1994.

7.
H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1949), 100-115. crossref(new window)

8.
V. Malovichko, A generalized hypergeometric function, and some integral operators that contain it, Mat. Fiz. Vyp. 19 (1976), 99-103.

9.
A. M. Mathai and R. K. Saxena, Generalized Hypergeometric Functions With Applications in Statistics and Physical Sciences, Springer-Verlag, Berlin, 1973.

10.
K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, Inc., 1993.

11.
R. K. Raina, On generalized Wright's hypergeometric functions and fractional calculus operators, East Asian Math. J. 21 (2005), no. 2, 191-203.

12.
E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

13.
S. B. Rao, J. C. Prajapati, A. D. Patel, and A. K. Shukla, On generalized hypergeometric function and fractional calculus, Communicated for publication.

14.
S. B. Rao, J. C. Prajapati, and A. K. Shukla, Generalized hypergeometric function and its properties, Communicated for publication.

15.
S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science publishers, Yverdon (Switzerland), 1993.

16.
N. Virchenko, On some generalizations of the functions of hypergeometric type, Fract. Calc. Appl. Anal. 2 (1999), no. 3, 233-244.

17.
N. Virchenko, On the generalized confluent hypergeometric function and its applications, Fract. Calc. Appl. Anal. 9 (2006), no. 2, 101-108.

18.
N. Virchenko, S. L. Kalla, and A. Al-Zamel, Some results on a generalized hypergeometric function, Integral Transform. Spec. Funct. 12 (2001), no. 1, 89-100. crossref(new window)

19.
N. Virchenko, O. Lisetska, and S. L. Kalla, On some fractional integral operators involving generalized Gauss hypergeometric functions, Appl. Appl. Math. 5 (2010), no. 10, 1418-1427.

20.
N. Virchenko and Olena V. Rumiantseva, On the generalized associated Legendre functions, Fract. Calc. Appl. Anal. 11 (2008), no. 2, 175-185.

21.
E. M. Wright, On the coefficient of the power series having exponential singularities, J. London Math. Soc. 8 (1933), 71-79.