Differences

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--- tangens [2015/06/30 10:43]
nikolaj old revision restored (2015/04/27 17:02)
+++ tangens [2015/06/30 10:47]
nikolaj
@@ Line 1: / Line 1: @@
 ===== Tangens =====
 ==== Function ====
->
+>todo
+$\tan(x):=\dfrac{\sin(x)}{\cos(x)}$
+$\tan(x)=\sum_{n=1}^\infty (-1)^{n-1}\frac{2^{2n} (2^{2n}-1)}{(2n)!}B_{2n}\,x^{2n-1}$
+with $B_k$ ... Bernoulli numbers
 -----
 === Theorems ===
-^ $\left(\dfrac{\tan(x)}{x}\right)^n=1+n\dfrac{1}{3}x^2+n\left(\dfrac{n}{18}+\dfrac{7}{90}\right)x^4+{\mathcal O}(x^6)$ ^
+^ $\left(\dfrac{\tan(x)}{x}\right)^m=1+m\dfrac{1}{3}x^2+m\left(\dfrac{m}{18}+\dfrac{7}{90}\right)x^4+{\mathcal O}(x^6)$ ^
 === References ===