An orthogonality relation for the Whittaker functions of the second kind of imaginary order
An orthogonality relation for the Whittaker functions of the second kind of imaginary order
复制标题
第二类虚阶Whittaker函数的正交关系
DOI：
10.1080/10652461003643412
复制
发表时间：
2009
影响因子：
1
通讯作者：
S. Bielski
中科院分区：
文献类型：
--
作者：
Radosław Szmytkowski;S. Bielski
研究了第二类虚级惠特克函数Wκ，Iμ(X)与μ∈ℝ的正交性。积分与和δ(μ−μ‘)+δ(μ+μ’成正比，其中δ(μ±μ‘是狄拉克三角洲分布。比例因子为π2/[μSinh(2πμ)Γ(1/2−κ+iμ)Γ(1/2−κ−Iμ)])。对于κ=0，导出的公式简化为最近文献中讨论的虚级Macdonald函数的正交性关系。
An orthogonality relation for the Whittaker functions of the second kind of imaginary order, W κ, iμ(x), with μ∈ℝ, is investigated. The integral is shown to be proportional to the sum δ(μ−μ′)+δ(μ+μ′), where δ(μ±μ′) is the Dirac delta distribution. The proportionality factor is found to be π2/[μsinh(2πμ) Γ(1/2−κ+iμ) Γ(1/2−κ−iμ)]. For κ=0, the derived formula reduces to the orthogonality relation for the Macdonald functions of imaginary order, discussed recently in the literature.