Binomial series
Mathematical series / From Wikipedia, the free encyclopedia
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In mathematics, the binomial series is a generalization of the polynomial that comes from a binomial formula expression like for a nonnegative integer . Specifically, the binomial series is the MacLaurin series for the function , where and . Explicitly,
-
(1)
where the power series on the right-hand side of (1) is expressed in terms of the (generalized) binomial coefficients
Note that if α is a nonnegative integer n then the xn + 1 term and all later terms in the series are 0, since each contains a factor of (n − n). Thus, in this case, the series is finite and gives the algebraic binomial formula.