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The question was asked: Is it possible to express the function \begin{equation} \tag{1.1} h(a)\equiv\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \label{question} \end{equation} in closed form? After considerable analysis, the answer appears to be "no", but during the attempt to answer this question, a number of interesting (and unexpected) related results were obtained, either as specialized transformations, or as closed-form expressions for several related functions.
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A new proof of the extended Saalschütz’s summation theorem for the series F 3 4 {}_{4}{F}_{3} and its application
Choi J. Rathie A. and P. Chopra · 2013
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