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Weierstrass Operator

The operator e^(nut^2/2) which satisfies

e^(nut^2/2)p(x)=1/(sqrt(2pinu))int_(-infty)^inftye^(-u^2/(2nu))p(x+u)du

for nu>0.

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References

Roman, S. The Umbral Calculus. New York: Academic Press, p. 88, 1984.Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.

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Weierstrass Operator

Cite this as:

Weisstein, Eric W. "Weierstrass Operator." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/WeierstrassOperator.html

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