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Mehler-Fock Transform

The integral transform defined by

g(x)=int_1^inftyt^(1/4-nu/2)(t-1)^(1/4-nu/2)P_(-1/2+ix)^(nu-1/2)(2t-1)f(t)dt

(Samko et al. 1993, p. 761) or

g(x)=int_1^inftyP_(-1/2+ix)^k(t)f(t)dt

(Samko et al. 1993, p. 24), where P_n(z) is a Legendre polynomial.

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References

Marichev, O. I. Eqn. 8.42 in Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables. Chichester, England: Ellis Horwood, 1982.Samko, S. G.; Kilbas, A. A.; and Marichev, O. I. Fractional Integrals and Derivatives. Yverdon, Switzerland: Gordon and Breach, pp. 24 and 761, 1993.

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Mehler-Fock Transform

Cite this as:

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

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