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Buschman Transform

The integral transform defined by

(Kphi)(x)=int_0^infty(x^2-t^2)_+^(lambda/2)P_nu^lambda(t/x)phi(t)dt,

where y_+^alpha is the truncated power function and P_nu^lambda(x) is an associated Legendre polynomial. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).

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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. 23, 1993.

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Buschman Transform

Cite this as:

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

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