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Steffensen Sequence

A sequence

s_n^((lambda))(x)=[h(t)]^lambdas_n(x),

where s_n(x) is a Sheffer sequence, h(t) is invertible, and lambda ranges over the real numbers. If s_n(x) is an associated Sheffer sequence, then s_n^((lambda)) is called a cross sequence. If s_n(x)=x^n, then

s_n^((lambda))(x)=[h(t)]^lambdax^n

is called an Appell cross sequence.

An example is the Laguerre polynomial.

See also

Appell Cross Sequence, Cross Sequence, Sheffer Sequence

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References

Brown, J. W. and Goldberg, J. L. "A Note on Generalized Appell Polynomials." Amer. Math. Monthly 75, 169-170, 1968.Roman, S. "Cross Sequences and Steffensen Sequences." §5.3 in The Umbral Calculus. New York: Academic Press, pp. 140-143, 1984.Rota, G.-C.; Kahaner, D.; and Odlyzko, A. "On the Foundations of Combinatorial Theory VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.

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Steffensen Sequence

Cite this as:

Weisstein, Eric W. "Steffensen Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteffensenSequence.html

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