Relations among the fundamental solutions of the generalized hypergeometric equation when $p = q + 1$. I. non-logarithmic cases
Relations among the fundamental solutions of the generalized hypergeometric equation when $p = q + 1$. I. non-logarithmic cases
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当$p = q 1$ 时广义超几何方程的基本解之间的关系。
DOI：
10.1090/s0002-9904-1938-06776-6
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发表时间：
1938
影响因子：
1.3
通讯作者：
F. C. Smith
中科院分区：
文献类型：
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作者：
F. C. Smith
^ r ( l at + ay) ^ r ( l c, + ay + w) 1 (3) F»,= 2r°'11 2̂ II ' <-ir ( l ct + ay) n==0 «-1 r ( l a* + ay + ») s" y = 1,2,. . . ,q+ l\\z\> 1。但是，如果我们假设 ci —• c\ — l\\ c% — C<L — h] ' • ' ; cr cr-i = /r_i 其中每个 lv 为零或正整数，同时假设这些 r ct 都不等于或不同于任何 at 整数，则作者证明解 (2) 的第一个 r 被替换为以下形式 [2] ：
^ r ( l at + ay) ^ r ( l c, + ay + w) 1 (3) F»,= 2r°'11 2̂ II ' <-i r ( l ct + ay) n==0 «-1 r ( l a* + ay + ») s" y = 1,2,. . . ,q+ l\\z\> 1. If, however, we assume that ci —• c\ — l\\ c% — C<L — h] ' • ' ; cr cr-i = /r_i where each lv is zero or a positive integer and assume at the same time that none of these r ct is equal to or differs from any of the at by an integer, then the author has shown that the first r of the solutions (2) are replaced by the following forms [2] :