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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