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单词 reduction formula
释义

reduction formula

Let In be some quantity that is dependent upon the natural number n. It may be possible to establish some general formula, expressing In in terms of some of the quantities In −1, In −2,…. Such a formula is a reduction formula and can be used to evaluate In for a particular value of n. The method is particularly useful in integration. For example, if

it can be shown, by integration by parts, that

As I0 = π/2, the reduction formula can be used, for example, to find that

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