Identities for the Hankel transform and their applications
Identities for the Hankel transform and their applications
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DOI：
10.1016/j.jmaa.2008.12.050
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发表时间：
2008-07
影响因子：
1.3
通讯作者：
A. Dernek;Neşe Dernek;O. Yúrekli
中科院分区：
文献类型：
--
作者：
A. Dernek;Neşe Dernek;O. Yúrekli
本文证明了Hankel变换与Kν变换的迭代是Widder变换的常数倍。利用这些迭代恒等式，给出了这类变换的几个Parseval-Goldstein型定理.利用这些结果得到了这些变换和拉普拉斯变换的若干新的Goldstein型交换恒等式。本文证明的恒等式为计算特殊函数的无穷积分提供了有用的推论。文中还给出了一些例子来说明本文的结果。
In the present paper the authors show that iterations of the Hankel transform with Kν-transform is a constant multiple of the Widder transform. Using these iteration identities, several Parseval–Goldstein type theorems for these transforms are given. By making use of these results a number of new Goldstein type exchange identities are obtained for these and the Laplace transform. The identities proven in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.