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A Generalisation of a Result of Abel with an Application to Tree Enumerations

Published online by Cambridge University Press:  20 January 2009

M. M. Robertson
M. M. Robertson
Affiliation:
Department of Mathematics, University of California, Los Angeles, U.S.A.
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We prove the following theorem, which was established by Abel (1) for the case u = 1.

Theorem. If u, k are positive integers and x, 1, , u, are real numbers, then

where the sum is taken over all distinct ordered solutions (s1, , su) in non-negative integers of the equation .

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 3 , June 1965 , pp. 239 - 241
Copyright
Copyright Edinburgh Mathematical Society 1965

References

REFERENCES

(1) Abel, N. H., Beweis eines Ausdruckes, von welchem die Binomial-Formel ein einzelner Fall ist, Journal fur die Reine und Angewandte Mathematik, 1 (1826), 159160Google Scholar