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On Abel's Binomial Identity

Published online by Cambridge University Press:  20 November 2018

Kulendra N. Majindar
Kulendra N. Majindar*
Affiliation:
Loyola College, Montreal
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The identity of Abel [1] [2] we deal with here can be stated in the following form: If n is a positive integer,

.

(In order that all terms be defined we require a ≠ 0, b ≠ n.)

This identity and deductions from it have been very useful in many problems, for instance in mathematical statistics [3]. Usually this identity is established by means of the Lagrange - Bűrman theorem [4]. Here we will derive it very simply.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 2 , June 1964 , pp. 301 - 303
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Abel, N. H., Oeuvres complètes, Vol. 1, p. 102.Google Scholar
2. Gould, H., Final Analysis of Vandermondes formula, Amer. Math. Monthly, Vol. 64(1957), pp. 409–415.Google Scholar
3. Birnbaum, Z. W. and Pyke, R., Annals of Math. Stat., Vol. 29 (1958), pp. 179–187.Google Scholar
4. Bromwich I' A, T.J., Introduction to the theory of infinite series. Google Scholar