Zeros of \({}_3 F_2\) hypergeoemtric polynomials (Q5939871)

The zeros of polynomials \(_2F_1[-n, b;c;z]\), where \(b\) is real and \(c\) is \({1\over 2}\) or \({3\over 2}\), have been discussed recently by Driver and Möller [J. Comput. Appl. Math. (to appear). These results are applied in the present paper to investigate the zeros of three \(_3F_2 [z]\) polynomials that are expressible as constant multiples of squares or products of polynomials of the above-mentioned type. The \(_3F_2\) polynomials are of even degree \(2n\) and contain one real parameter \(b\). The location of the zeros as \(b\) varies is given in three theorems. In addition, numerical tables of the zeros, generated by MATHEMATICA, are presented.