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Generalizations of Dixon’s theorem on the sum of a \(_ 3F_ 2\). (English) Zbl 0793.33006

This paper is similar to that of the preceding review. The authors obtain the sums of the series \[ _ 3F_ 2\left[ \left. \begin{matrix} a,\;b,\;c \\ 1+a-b+i,\;1+a-c+i+j \end{matrix} \right | 1 \right] \] for small values of the integers \(i\) and \(j\). Moreover, they consider the limiting cases \(c=m\), \(i+j \geq m\), where \(m\) is an integer. The results are, again, given as master formulas supplemented by tables of coefficients.

MSC:

33C20 Generalized hypergeometric series, \({}_pF_q\)
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