Evaluation of a class of binomial coefficient summations
نویسندگان
چکیده
منابع مشابه
Evaluation of a Class of Binomial Coefficient Summations
In this paper we prove the fo rmula ~o w ~-dk (Pn-bkk)(q +k bk) ( _ 1 ) k (p --kbW/d) (k q-kW/d) -I (p + q -k =kffio n k / and ob ta in a more general t r ans fo rma t ion for s u m s of the fo rm ~ (a +kbk) (c + b(n-k))f(k)g(n -k ). k=o n k These sums con ta in m a n y special cases in the l i terature of statistics, probabili ty, combinator ia l analysis, special funct ions , and o ther areas...
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Denote by x a random innnite path in the graph of Pascal's triangle (left and right turns are selected independently with xed probabilities) and by d n (x) the binomial coeecient at the n'th level along the path x. Then for a dense G set of in the unit interval, fd n (x)g is almost surely dense but not uniformly distributed modulo 1.
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Denote by x a random infinite path in the graph of Pascal’s triangle (left and right turns are selected independently with fixed probabilities) and by dn(x) the binomial coefficient at the n’th level along the path x. Then for a dense Gδ set of θ in the unit interval, {dn(x)θ} is almost surely dense but not uniformly distributed modulo 1.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1966
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(66)80030-3