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Reduction Formula


A reduction formula is a recurrence relation that expresses a member of a parametrized family of quantities in terms of members with smaller parameter values. Reduction formulas are especially common for integrals and permit repeated reduction to one or more initial cases. For example, integration by parts gives

 I_n=int_0^(pi/2)sin^nxdx=(n-1)/nI_(n-2),

for n>=2, with I_0=pi/2 and I_1=1.


See also

Definite Integral, Integration by Parts, Recurrence Equation, Recurrence Relation

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.

Cite this as:

Weisstein, Eric W. "Reduction Formula." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ReductionFormula.html

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