Darboux's formula
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Darboux's formula is a mathematical formula used in analysis for the purpose of summing infinite series 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.
The formula is due to French mathematician Jean Gaston Darboux and was first published in 1876 in Liouville's Journal.
[edit] References
- Whittaker, E. T. and Watson, G. N. "A Formula Due to Darboux." §7.1 in A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, p. 125, 1990. [1]
