Expansions of hypergeometric functions in hypergeometric functions
Expansions of hypergeometric functions in hypergeometric functions
复制标题
超几何函数中超几何函数的展开
DOI：
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发表时间：
1961
期刊：
影响因子：
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通讯作者：
J. Wimp
中科院分区：
文献类型：
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作者：
J. Fields;J. Wimp
在（1）中，Luke给出了合流超几何函数关于修正Bessel函数I（z）的一个展开式。其他类似扩张的存在意味着可能存在更普遍的扩张。事实就是如此。本文利用拉普拉斯变换技巧推广了低阶超几何函数关于其它超几何函数的乘法型展开式。1.一般扩展。广义超几何函数pFq（z），（2）定义为~~~~~~~~~~~~~~~~P KF~~~~~~~~~~~~~~~~~（Z）= Z）~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I（ai）~~~
In (1) Luke gave an expansion of the confluent hypergeometric func- tion in terms of the modified Bessel functions I,(z). The existence of other, similar expansions implied that more general expansions might exist. Such was the case. Here multiplication type expansions of low-order hypergeometric functions in terms of other hypergeometric functions are generalized by Laplace transform techniques. 1. General Expansions. The generalized hypergeometric function pFq(z), (2), is defined by ~~~~~~~~~~~~P KF~~~~~~~~~(Z) = Z) ~~~~~~~~~~~~~~~~~~~~~~~~~~~ I~~~~~I (ai)~