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| Funktion | Potenzreihe | Konvergenz |
| (1 ± x)m | 1 ± mx +  x2 ± + … | |x|≤ 1 |
+(±1)n xn + … | ||
| sin(x + Δx) | sin(x) +  cos(x) +  f′′(x) + … | |Δx| < ∞ |
+ sin(x +  ) + … | ||
| cos(x + Δx) | cos(x) − Δx sin(x) − +  | |Δx| < ∞ |
+ −… +  ±… | ||
| tan x | x +  x3 +  x5 +  x7 +  x9… | |x| <  |
| cot x |  −![[ x x3 2x5- -x7- ]
3 + 45 + 945 + 4725 ...](el-20171820x.png) | 0 < |x| < π |
| ex | 1 +  +  +  +  + … | |x| < ∞ |
| ax = exln a | 1 +  +  +  +  + … | |x| < ∞ |
| ln x | 2 | x > 0 |
![2n+1 ]
+ (2n(+x−1)(1x)+1)2n+1 + ...](el-20171830x.png) | ||
| ln x | (x − 1) − +  + … | 0 < x ≤ 2 |
+(−1)n+1 + … | ||
| ln x |  +   2 +   3 + … | x >  |
+  n + … | ||
| ln(1 + x) | x − +  − + … | −1 < x ≤ 1 |
+(−1)n+1 + … | ||
| arcsin x | x +  +  +  + … | |x| < 1 |
| arccos x |  −![[ ]
x + -x3-+ 1·3x5- + 1·3-·5x5-+ ...
2·3 2·4·5 2·4·6 ·7](el-20171850x.png) | |x| < 1 |
| arctan x | x − +  −… + (−1)n + … | |x| < 1 |
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