Notions of orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral representations, orthogonality relations and explicit expressions are established.

中文翻译：

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通过Kontorovich-Lebedev变换的正交性和卷积正交性

使用Kontorovich-Lebedev变换及其卷积来探索正交性和卷积正交性的概念。研究了相应的正交多项式和函数的新类别。建立了整体表示，正交关系和显式表达式。