The forward and inverse Kontorovich-Lebedev transforms are defined by
![K_(ix)[f(t)]](/images/equations/Kontorovich-LebedevTransform/Inline1.svg) |  |  |
(1)
|
![K_(ix)^(-1)[g(t)]](/images/equations/Kontorovich-LebedevTransform/Inline4.svg) |  |  |
(2)
|
respectively, where 
is a modified
Bessel function of the second kind with imaginary index 
.
Kontorovich-Lebedev Transform
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References
Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, p. 753, 1993.Referenced on Wolfram|Alpha
Kontorovich-Lebedev TransformCite this as:
Weisstein, Eric W. "Kontorovich-Lebedev Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kontorovich-LebedevTransform.html