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Series multisection : ウィキペディア英語版
Series multisection
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
: \sum_^\infty a_n\cdot x^n
then its multisection is a power series of the form
: \sum_^\infty a_\cdot x^
where ''c'', ''d'' are integers, with 0 ≤ ''d'' < ''c''.
== Multisection of analytic functions ==
A multisection of the series of an analytic function
: F(x) = \sum_^\infty a_n\cdot x^n
has a closed-form expression in terms of the function F(x):
: \sum_^\infty a_\cdot x^ = \tfrac\cdot \sum_^ w^\cdot F(w^k\cdot x),
where w = e^} is a primitive ''c''-th root of unity.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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