抄録
The Gauss contiguous relations are used to give three recurrence relations for the hypergeometric functions F (n +a,n +b ;m +c ;z ) for integers n and m. Their usefulness in successive computation of F (n +1⁄2,n +1⁄2;m ;z ) and its analytic continuation is studied for integers n and m satisfying n ≥ 0 and m > 0, for complex numbers z. A program in C language is presented, by which all the values of F (n +1⁄2,n +1⁄2;m ;z ) for n and m satisfying 0 ≤ n ≤ n 1 and 1 ≤ m ≤ m 1 are calculated when positive integers n 1 and m 1 and a complex number z are given; the algorithm is applicable to the analytic continuation of the function. The algorithm for the computation of F (n +a,n +b ;m +c ;z ) is sketched.
