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Stieltjes Transform

The integral transform

(Kf)(x)=Gamma(p)int_0^infty(x+t)^(-p)f(t)dt.

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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Stieltjes Transform

Cite this as:

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

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