Some inequalities for the Gauss and Kummer hypergeometric functions (Q1184898)

Using the relations between contiguous functions, one may write \(_ 2F_ 1(a+n+1,b;c;x)\) as an \((n+2)\times (n+2)\) determinant, to which known inequalities may be applied. This is the idea behind Theorem 1, the statement of which is, however, confusing: only several pages hence does the reader realize what is meant. Theorem 2, which is based upon the same idea, is an improvement of a previous result given by the authors [Math. Comput. 38, 201-205 (1982; Zbl 0485.33001)]. There are four more theorems, which involve \(\psi (a;b;x)\), \(_{p+1}F_ p\), and \(_ pF_ p\). They are straightforward applications and improvements of known results.