Euler–Maclaurin formula
theorem
Facts
5 properties- Defining formula
- \sum\limits_{a \leqslant k <b}f(k) = \int\limits_a^b f(x)dx + \left.\sum\limits_{k=1}^m \frac{B_k}{k!}f^{(k-1)}(x)\right|_a^b + R_m, R_m=(-1)^{m+1}\int\limits_a^b\frac{B_m(\{x\})}{m!}f^{(m)}(x)dx
- Maintained by WikiProject
- WikiProject Mathematics
- Named after
- Leonhard Euler, Colin MacLaurin
- Studied by
- approximation theory
🏷️ Also known as
en Euler–Maclaurin formula
ar صيغة أويلر-ماكلورين
cs Eulerův–Maclaurinův vzorec
da Euler-Maclaurins formel
de Euler-Maclaurin-Formel
es formula de Euler-Maclaurin
es fórmula de Euler-Maclaurin
fr formule d'Euler-Maclaurin
he נוסחת אוילר-מקלורן
hu Euler-Maclaurin képlet
it formula di Eulero-Maclaurin
ja オイラーの和公式
ko 오일러-매클로린 공식
nl Formule van Euler-Maclaurin
pl Wzór Eulera-Maclaurina
pt Fórmula Euler–Maclaurin
ru формула суммирования Эйлера — Маклорена
ru формула Эйлера — Маклорена
ru формула Эйлера-Маклорена
uk формула Ейлера — Маклорена
🔖 Identifiers · 3
- Freebase ID
- /m/02mjj
- MathWorld ID
- Euler-MaclaurinIntegrationFormulas
- Microsoft Academic ID (discontinued)
- 51074892
🔗 Connections
Named after 2
Created notable works 1
Maintained by WikiProject 1
Studied by 1
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Summary
Euler–Maclaurin formula is a formula[1].
Key Facts
- Instance of: theorem[2]
- Named after: Leonhard Euler[3], Colin MacLaurin[4]
- Euler–Maclaurin formula's defining formula is recorded as \sum\limits_{a \leqslant k <b}f(k) = \int\limits_a^b f(x)dx + \left.\sum\limits_{k=1}^m \frac{B_k}{k!}f^{(k-1)}(x)\right|a^b + R_m, R_m=(-1)^{m+1}\int\limits_a^b\frac{B_m({x})}{m!}f^{(m)}(x)dx<sup id="cite-C15" class="cite-ref" title="Euler–Maclaurin formula — defining formula (P2534): \sum\limits{a \leqslant k
- Studied by: approximation theory[5]
- Maintained by WikiProject: WikiProject Mathematics[6]