Series multisection

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

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.

Example[edit]

Multisection of a binomial

at x = 1 gives the following identity for the sum of binomial coefficients with step c:

References[edit]