TOPICS
Search

Love Transform

The integral transform

(Kf)(x)=int_0^infty((x-t)_+^(c-1))/(Gamma(c))_2F_1(a,b;c;1-t/x)f(t)dt,

where Gamma(x) is the gamma function, _2F_1(a,b;c;z) is a hypergeometric function, where y_+^alpha denotes the truncated power function. Note the lower limit of 0, not -infty as implied in Samko et al. (1993, p. 23, eqn. 1.101).

Explore with Wolfram|Alpha

References

Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, p. 23, 1993.

Referenced on Wolfram|Alpha

Love Transform

Cite this as:

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

Subject classifications