Some families of generalized complete and incomplete elliptic-type integrals


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.


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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


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