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Integration by reduction formula in integral calculus is a technique of integration, in the form of a recurrence relation. It is used when an expression containing an integer parameter, usually in the form of powers of elementary functions, or products of transcendental functions and polynomials of arbitrary degree, can't be integrated directly. But using other methods of integration a reduction formula can be set up to obtain the integral of the same or similar expression with a lower integer parameter, progressively simplifying the integral until it can be evaluated. 〔Mathematical methods for physics and engineering, K.F. Riley, M.P. Hobson, S.J. Bence, Cambridge University Press, 2010, ISBN 978-0-521-86153-3〕 This method of integration is one of the earliest used. == How to find the reduction formula == The reduction formula can be derived using any of the common methods of integration, like integration by substitution, integration by parts, integration by trigonometric substitution, integration by partial fractions, etc. The main idea is to express an integral involving an integer parameter (e.g. power) of a function, represented by In, in terms of an integral that involves a lower value of the parameter (lower power) of that function, for example ''I''''n''-1 or ''I''''n''-2. This makes the reduction formula a type of recurrence relation. In other words, the reduction formula expresses the integral : in terms of : where : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Integration by reduction formulae」の詳細全文を読む スポンサード リンク
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