In mathematics, a multisection of a power series is a new power series composed of equally spaced terms extracted unaltered from the original series. Formally, if one is given a power series
then its multisection is a power series of the form
where c, d are integers, with 0 ≤ d < c.
Multisection of analytic functions
A multisection of the series of an analytic function
has a closed-form expression in terms of the function :
where is a primitive c-th root of unity.
Multisection of a binomial expansion
at x = 1 gives the following identity for the sum of binomial coefficients with step c: