On Certain Hypergeometric Summation Theorems Motivated by the Works of Ramanujan, Chudnovsky and Borwein

M. I. Qureshi, Izharul H. Khan, M. P. Chaudhary

Abstract


In the present paper, we obtain numerical values for Gaussian
hypergeometric summation theorems by giving particular values to the
parameters $a,~b$ and the argument $x$; three summation theorems for
${}_{2}F_{3}(\frac{1}{4},\frac{3}{4};\frac{1}{2},\frac{1}{2},1;x)$,
three summation theorems for
${}_{4}F_{3}(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{a+b}{b};1,1,\frac{a}{b};x)$,
two summation theorems for
${}_{4}F_{3}(\frac{1}{2},\frac{1}{3},\frac{2}{3},\frac{a+b}{b};1,1,\frac{a}{b};x)$,
four summation theorems for
${}_{4}F_{3}(\frac{1}{2},\frac{1}{6},\frac{5}{6},\frac{a+b}{b};1,1,\frac{a}{b};x)$
and ten summation theorems for
${}_{4}F_{3}(\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{a+b}{b};1,1,\frac{a}{b};x)$.


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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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