Some families of generalized complete and incomplete elliptic-type integrals
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Authors
H. M. Srivastava
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China.
R. K. Parmar
- Department of Mathematics, Government College of Engineering and Technology, Bikaner 334004, Rajasthan, India.
P. Chopra
- Department of Mathematics, Marudhar Engineering College, Bikaner 334001, Rajasthan, India.
Abstract
Analogous to the recent generalizations of the familiar beta and hypergeometric functions by Lin et al. [S.-D. Lin, H. M.
Srivastava, J.-C. Yao, Appl. Math. Inform. Sci., 9 (2015), 1731–1738], the authors introduce and investigate some general families
of the elliptic-type integrals for which the usual properties and representations are naturally and simply extended. The object of
the present paper is to study these generalizations and their relationships with generalized hypergeometric functions of one, two
and three variables. Moreover, the authors establish the Mellin transform formulas and various derivative and integral properties
and obtain several relations for special cases in terms of well-known higher transcendental functions and some infinite series
representations containing the Meijer G-function, the Whittaker function and the complementary error functions, as well as the
Laguerre polynomials and the products thereof. A number of (known or new) special cases and consequences of the main results
presented here are also considered.
Share and Cite
ISRP Style
H. M. Srivastava, R. K. Parmar, P. Chopra, Some families of generalized complete and incomplete elliptic-type integrals, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1162--1182
AMA Style
Srivastava H. M., Parmar R. K., Chopra P., Some families of generalized complete and incomplete elliptic-type integrals. J. Nonlinear Sci. Appl. (2017); 10(3):1162--1182
Chicago/Turabian Style
Srivastava, H. M., Parmar, R. K., Chopra, P.. "Some families of generalized complete and incomplete elliptic-type integrals." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1162--1182
Keywords
- Incomplete and complete elliptic integrals
- generalized Beta function
- generalized hypergeometric functions
- generalized Appell functions
- generalized Lauricella functions
- Mellin transforms
- Whittaker functions
- Laguerre polynomials.
MSC
- 26A33
- 33C65
- 33C75
- 78A40
- 78A45
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