@article {
author = {Rakha, M. A. and Rathie, A. K. and Chopra, P.},
title = {ON AN EXTENSION OF A QUADRATIC TRANSFORMATION FORMULA DUE TO GAUSS},
journal = {International Journal of Mathematical Modelling & Computations},
volume = {1},
number = {3 (SUMMER)},
pages = {171-174},
year = {2011},
publisher = {Islamic Azad University, Central tehran Branch},
issn = {2228-6225},
eissn = {2228-6233},
doi = {},
abstract = {The aim of this research note is to prove the following new transformation formula \begin{equation*} (1-x)^{-2a}\,_{3}F_{2}\left[\begin{array}{ccccc} a, & a+\frac{1}{2}, & d+1 & & \\ & & & ; & -\frac{4x}{(1-x)^{2}} \\ & c+1, & d & & \end{array}\right] \\ =\,_{4}F_{3}\left[\begin{array}{cccccc} 2a, & 2a-c, & a-A+1, & a+A+1 & & \\ & & & & ; & -x \\ & c+1, & a-A, & a+A & & \end{array} \right], \end{equation*} where $A^2=a^2-2ad+cd$ after the equation. For d=c, we get a known quadratic transformations due to Gauss. The result is derived with the help of the generalized Gauss's summation theorem available in the literature.},
keywords = {Gauss hypergeometric function,2F1 Hypergeometric function,Contiguous function relation,Linear recurrence relation},
url = {http://ijm2c.iauctb.ac.ir/article_521707.html},
eprint = {http://ijm2c.iauctb.ac.ir/article_521707_6ff9c3eeb7305ab8c3f88028bac474be.pdf}
}