TITLE:
The Series of Reciprocals of Non-central Binomial Coefficients
AUTHORS:
Laiping Zhang, Wanhui Ji
KEYWORDS:
Binomial Coefficients; Split Terms; Reciprocals; Series; Non-central; Closed Form
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.3 No.3B,
October
25,
2013
ABSTRACT:
Utilizing Gamma-Beta function, we can build one
series involving reciprocal of non-central binomial coefficients, then We can
structure several new series of reciprocals of non-central binomial
coefficients by item splitting, these new created denominator of series contain
1 to 4 odd factors of binomial coefficients. As the result of splitting items,
some identities of series of numbers values of reciprocals of binomial
coefficients are given. The method of splitting terms offered in this paper is
a new combinatorial analysis way and elementary method to create new series.