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binomial coefficient
(redirected from Binomial coefficients)

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binomial coefficient [bī′nō·mē·əl kō·ə′fish·ənt]
(mathematics)
A coefficient in the expansion of (x + y)n, wherenis a positive integer; the (k + 1)st coefficient is equal to the number of ways of choosingkobjects out ofnwithout regard for order. Symbolized (nk);nCk;C(n,k);Cnk.


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For the sake of completeness we give, without proof, two particular theorems in regard to single binomial coefficients and their integral representations.
Permutations and combinations, Binomial theorem for a positive integral index, properties of binomial coefficients.
The [gamma]-operators bypass the trace calculations of (2) that were used to evaluate the in-between (3,1)-case and consequently the evaluation of the Hankel determinant of binomial coefficients [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] This Hankel determinant was evaluated as an almost product in (2).
 
 
 
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