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Abel's Binomial Theorem

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The identity

sum_(y=0)^m(m; y)(w+m-y)^(m-y-1)(z+y)^y=w^(-1)(z+w+m)^m

(Bhatnagar 1995, p. 51). There are a host of other such binomial identities.

See also

Binomial Identity, q-Abel's Theorem

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References

Abel, N. H. "Beweis eines Ausdrucks, von welchem die Binomial-Formel ein einzelner Fall ist." J. reine angew. Math. 1, 159-160, 1826. Reprinted in Œuvres Complètes, 2nd ed., Vol. 1. pp. 102-103, 1881.Bhatnagar, G. Inverse Relations, Generalized Bibasic Series, and their U(n) Extensions. Ph.D. thesis. Ohio State University, p. 51, 1995.Riordan, J. Combinatorial Identities. New York: Wiley, p. 18, 1979.

Referenced on Wolfram|Alpha

Abel's Binomial Theorem

Cite this as:

Weisstein, Eric W. "Abel's Binomial Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelsBinomialTheorem.html

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