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http://dx.doi.org/10.5831/HMJ.2016.38.4.693

A DERIVATION OF TWO QUADRATIC TRANSFORMATIONS CONTIGUOUS TO THAT OF KUMMER VIA A DIFFERENTIAL EQUATION APPROACH  

Shani, K. (Department of Mathematics, School of Mathematical and Physical Sciences,Central University of Kerala)
Choi, Junesang (Department of Mathematics, Dongguk University)
Rathie, Arjun K. (Department of Mathematics, School of Mathematical and Physical Sciences,Central University of Kerala)
Publication Information
Honam Mathematical Journal / v.38, no.4, 2016 , pp. 693-699 More about this Journal
Abstract
The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.
Keywords
Gauss hypergeometric function; quadratic transformation; hypergeometric differential equation;
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  • Reference
1 G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications 71, Cambridge University Press, Cambridge, 1999.
2 Y. S. Kim, A quadratic transformation due to Kummer, Annals of Korea 16 (1999), 223-226.
3 Y. S. Kim, M. A. Rakha and A. K. Rathie, Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), 387-402.   DOI
4 Y. L. Luke, The Special Functions and their Approximations 1, Academic Press, New York, 1969.
5 F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark (editors), NIST Handbook of Mathematical Functions, National Institute of Standards and Technology and Cambridge University Press, 2010.