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Cauchy formula for repeated integration
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<p>The Cauchy formula for repeated integration, named after <a href="/facts/Augustin-Louis_Cauchy/aoTjgj6j">Augustin-Louis Cauchy</a>, allows one to compress <i>n</i> <a href="/facts/Antidifferentiation/5qDsudIv">antiderivatives</a> of a function into a single integral (cf. <a href="/facts/Antiderivative/5qDsudIv">Cauchy's formula</a>). For non-integer <i>n</i> it yields the definition of <a href="/facts/Fractional_integral/PxN1pMcj">fractional integrals</a> and (with <i>n</i> < 0) <a href="/facts/Fractional_derivative/PxN1pMcj">fractional derivatives</a>. </p>