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- matematikai tétel (hu)
- théorème d'analyse (fr)
- benadering van een functie door een afgekapte machtreeks (nl)
- Funktionalapproximation durch ein Polynom (de)
- approximation of a function by a truncated power series (en)
- k 回微分可能な関数の与えられた点のまわりでの近似を k 次のテイラー多項式によって与える定理 (ja)
- przybliżenie funkcji wielomianem (pl)
- aproximarea funcțiilor cu o serie polinomială trunchiată (ro)
- مبرهنة في التحليل الرياضي (ar)
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- Let (en)
- . Then there exists a function (en)
- Let k ≥ 1 be an integer and let the function (en)
- a ∈ R (en)
- be k times differentiable at the point (en)
- f : R → R (en)
- hk : R → R (en)
- such that
and
This is called the Peano form of the remainder. (en)
- Let be a -times continuously differentiable function at the point . Then there exist functions , where such that (en)
- be k + 1 times differentiable on the open interval between and with f continuous on the closed interval between and . Then
for some real number between and . This is the Lagrange form of the remainder.
Similarly,
for some real number between and . This is the Cauchy form of the remainder.
Both can be thought of as specific cases of the following result: Consider
for some real number between and . This is the Schlömilch form of the remainder . The choice is the Lagrange form, whilst the choice is the Cauchy form. (en)
- Let be absolutely continuous on the closed interval between and . Then (en)
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- Integral form of the remainder (en)
- Mean-value forms of the remainder (en)
- Multivariate version of Taylor's theorem (en)
- Taylor's theorem (en)
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- Taylor's theorem (en)
- مبرهنة تايلور (ar)
- Teorema de Taylor (ca)
- Taylor-Formel (de)
- Teorema de Taylor (es)
- Théorème de Taylor (fr)
- Teorema di Taylor (it)
- Teorema Taylor (in)
- テイラーの定理 (ja)
- 테일러 정리 (ko)
- Stelling van Taylor (nl)
- Wzór Taylora (pl)
- Teorema de Taylor (pt)
- Теорема Тейлора (ru)
- Теорема Тейлора (uk)
- 泰勒公式 (zh)
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