Use of the Gauss Contiguous Relations in Computing the Hypergeometric Functions F (n +1/2,n +1/2;m ;z )
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概要
- 論文の詳細を見る
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.
- 東北大学の論文
- 1996-03-00
著者
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Morita Tohru
Department Of Applied Science Faculty Of Enginccring Tohoku University
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Morita Tohru
Department Of Computer And Mathematical Sciences Graduate School Of Information Sciences Tohoku Univ
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