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de Rham's Function

deRhamsFunction

de Rham's function is the function defined by the functional equations

phi_alpha(1/2x)=alphaphi_alpha(x)
(1)
phi_alpha(1/2(x+1))=alpha+(1-alpha)phi_alpha(x)
(2)

(Trott 2004, pp. 23-24).

See also

Functional Equation

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References

Berg, L. and Krüppel, M. "De Rham's Singular Function and Related Functions." Z. Anal. Anwendungen 19, 227-237, 2000.Berg, L. and Krüppel, M. "De Rham's Singular Function, Two-Scale Difference Equations and Appell Polynomials." Resul. Math. 38, 18-47, 2000.Kairies, H.-H. "Functional Equations for Peculiar Functions." Aeq. Math. 53, 207-241, 1997.Trott, M. The Mathematica GuideBook for Programming. New York: Springer-Verlag, 2004. http://www.mathematicaguidebooks.org/.

Referenced on Wolfram|Alpha

de Rham's Function

Cite this as:

Weisstein, Eric W. "de Rham's Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/deRhamsFunction.html

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