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http://dx.doi.org/10.4134/CKMS.c160043

GENERATING FUNCTIONS FOR THE EXTENDED WRIGHT TYPE HYPERGEOMETRIC FUNCTION  

Jana, Ranjan Kumar (Department of Applied Mathematics & Humanities S.V. National Institute of Technology)
Maheshwari, Bhumika (Department of Applied Mathematics & Humanities S.V. National Institute of Technology)
Shukla, Ajay Kumar (Department of Applied Mathematics & Humanities S.V. National Institute of Technology)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.1, 2017 , pp. 75-84 More about this Journal
Abstract
In recent years, several interesting families of generating functions for various classes of hypergeometric functions were investigated systematically. In the present paper, we introduce a new family of extended Wright type hypergeometric function and obtain several classes of generating relations for this extended Wright type hypergeometric function.
Keywords
generating functions; gamma and beta functions; hypergeometric functions; Wright type hypergeometric function; linear; bilinear and bilateral (or mixed multilateral) generating functions;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 M. A. Chaudhry and S. M. Zubair, Generalized incomplete gamma functions with applications, J. Comput. Appl. Math. 55 (1994), no. 1, 99-123.   DOI
2 M. A. Chaudhry and S. M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman and Hall/CRC, Boca Raton, 2002.
3 M. Dotsenko, On some applications of Wright's hypergeometric function, C. R. Acad. Bulgare Sci. 44 (1991), no. 6, 13-16.
4 A. Erdelyi, W. Mangus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions. Vol I, McGraw-Hill, New York, 1953.
5 V. Malovichko, On a generalized hypergeometric function and some integral operators, Math. Phys. 19 (1976), 99-103.
6 R. K. Parmar, Extended-hypergeometric functions and associated properties, C. R. Math. Acad. Sci. Paris 353 (2015), no. 5, 421-426.   DOI
7 E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.
8 S. B. Rao, A. D. Patel, J. C. Prajapati, and A. K. Shukla, Some properties of generalized hypergeometric function, Commun. Korean Math. Soc. 28 (2013), no. 2, 303-317.   DOI
9 H. M. Srivastava, A. Cetinkaya, and I. Onur Kymaz, A certain generalized Pochhammer symbol and its applications to hypergeometric functions, Appl. Math. Comput. 226 (2014), 484-491.
10 H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited), New York, 1984.
11 H. M. Srivastava, R. K. Parmar, and P. Chopra, A class of extended fractional derivative oper ators and associated generating relations involving hypergeometric functions, Axioms 1 (2012), no. 3, 238-258.   DOI
12 E. M. Wright, On the coefficient of power series having exponential singularities, J. Lond. Math. Soc. 5 (1933), no. 1, 71-79.
13 R. Srivastava, Some generalizations of Pochhammer's symbol and their associated families of hypergeometric functions and hypergeometric polynomials, Appl. Math. Inf. Sci. 7 (2013), no. 6, 2195-2206.   DOI
14 R. Srivastava, Some classes of generating functions associated with a certain family of extended and generalized hypergeometric functions, Appl. Math. Comput. 243 (2014), 132-137.
15 N. Virchenko, S. L. Kalla, and A. Al-Zamel, Some results on a generalized hypergeometric function, Integral Transforms Spec. Funct. 12 (2001), no. 1, 89-100.   DOI
16 S. B. Rao and A. K. Shukla, Note on generalized hypergeometric function, Integral Transforms Spec. Funct. 24 (2013), no. 11, 896-904.   DOI