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Darboux's formula : ウィキペディア英語版 | Darboux's formula
In mathematical analysis, Darboux's formula is a formula introduced by for summing infinite series by using integrals or evaluating integrals using infinite series. It is a generalization to the complex plane of the Euler–Maclaurin summation formula, which is used for similar purposes and derived in a similar manner (by repeated integration by parts of a particular choice of integrand). Darboux's formula can also be used to derive the Taylor series of the calculus. ==Statement== If φ(''t'') is a polynomial of degree ''n'' and ''f'' an analytic function then : The formula can be proved by repeated integration by parts.
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