This paper gives rapid proofs of two binomial coefficient identities found by Rosenbaum [J. Math. Phys. 8, 1977 (1967)] who obtained the identities from rather involved considerations of commutation relations. The present proofs make use of the Vandermonde convolution, or addition, theorem and a well‐known fact that the kth difference of a polynomial of degree k − 1 is zero. In a sense the two special cases are not essentially new.
REFERENCES
1.
2.
I. J. Schwatt, Operations with Series (The University of Pennsylvania Press, Philadelphia, Pa., 1924;
reprinted by Chelsea Publ. Co., New York, 1962).
3.
C. Jordan, Calculus of Finite Differences (Chelsea Publ. Co., New York, 1950).
4.
Editorial comment on
Math. Mag.
39
, 157
(1966
).5.
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© 1969 The American Institute of Physics.
1969
The American Institute of Physics
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