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Kontorovich-Lebedev Transform


The forward and inverse Kontorovich-Lebedev transforms are defined by

K_(ix)[f(t)]=int_0^inftyK_(ix)(t)f(t)dt
(1)
K_(ix)^(-1)[g(t)]=2/(pi^2x)int_0^inftytsinh(pit)K_(it)(x)g(t)dt,
(2)

respectively, where K_nu(z) is a modified Bessel function of the second kind with imaginary index nu=ix.


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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 Transform

Cite this as:

Weisstein, Eric W. "Kontorovich-Lebedev Transform." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kontorovich-LebedevTransform.html

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