ABSTRACT
The Kontorovich-Lebedev transform was introduced by the Soviet mathematicians M. J. Kontorovich and N. N. Lebedev in 1938-1939 [128] to solve certain boundary-value problems. The mathematical theory and the inversion formulas were later introduced by Lebedev in 1946 and 1949[139,140]; for a generalization and some related material see https://www.w3.org/1998/Math/MathML"> [ 116,137,138 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq6798.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> . The Kontorovich-Lebedev transform arises naturally when one uses the method of separation of variables to solve boundary-value problems formulated in terms of cylindrical coordinate systems. Therefore, it comes as no surprise that many more applications of it have been discovered in recent years.
