| dbo:abstract |
Darbouxův vzorec je v matematické analýze vzorec, který objevil Jean Gaston Darboux pro sumaci nekonečné řady pomocí integrálů nebo vyhodnocování integrálů pomocí nekonečné řady. Je zobecněním Eulerova–Maclaurinova sumačního vzorce na komplexní rovinu. Ten se používá pro podobné účely a odvozuje se podobným způsobem (opakovanou integrací per partes určité volby integrálu). Darbouxův vzorec lze použít pro odvození Taylorovy řady v infinitezimálním počtu. (cs) In mathematical analysis, Darboux's formula is a formula introduced by Gaston Darboux 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 from calculus. (en) |
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http://gallica.bnf.fr/ark:/12148/bpt6k16420b/f291%7Cvolume=3%7Cissue=II%7Cpages=291%E2%80%93312%7Cjournal= http://mathworld.wolfram.com/DarbouxsFormula.html https://books.google.com/books%3Fid=_hoPAAAAIAAJ&pg=PA96&lpg=PA96&dq=darboux's+formula&source=web&ots=-hSlgJrJXo&sig=8cg5JvFAW5r-7m9CPc2vIh5AtAc |
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dbr:Calculus dbr:Euler–Maclaurin_summation_formula dbr:Complex_plane dbr:MathWorld dbr:Mathematical_analysis dbr:E._T._Whittaker dbr:Euler–Maclaurin_formula dbr:Taylor_series dbc:Mathematical_analysis dbc:Summability_methods dbr:Summation dbr:Integral dbr:Integration_by_parts dbr:Infinite_series dbr:Integrand dbr:Bernoulli_polynomial |
| dbp:authorlink |
Jean Gaston Darboux (en) |
| dbp:date |
March 2022 (en) |
| dbp:first |
Gaston (en) |
| dbp:last |
Darboux (en) |
| dbp:reason |
This could only be true if a proof of Darboux's formula that DOES NOT RELY on the Taylor series, since otherwise such a proof deriving the Taylor series would be circular. Is it actually the case that Darboux's formula does not use the Taylor series? (en) |
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dbc:Mathematical_analysis dbc:Summability_methods |
| gold:hypernym |
dbr:Formula |
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| rdfs:comment |
Darbouxův vzorec je v matematické analýze vzorec, který objevil Jean Gaston Darboux pro sumaci nekonečné řady pomocí integrálů nebo vyhodnocování integrálů pomocí nekonečné řady. Je zobecněním Eulerova–Maclaurinova sumačního vzorce na komplexní rovinu. Ten se používá pro podobné účely a odvozuje se podobným způsobem (opakovanou integrací per partes určité volby integrálu). Darbouxův vzorec lze použít pro odvození Taylorovy řady v infinitezimálním počtu. (cs) In mathematical analysis, Darboux's formula is a formula introduced by Gaston Darboux 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 from calculus. (en) |
| rdfs:label |
Darbouxův vzorec (cs) Darboux's formula (en) |
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dbr:Christoffel–Darboux_formula |
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