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sine_function [2015/07/03 15:51]
nikolaj
sine_function [2015/11/04 16:24]
nikolaj
Line 12: Line 12:
  
 == Theorem == == Theorem ==
-From + 
 +  * From 
 $\sum_{n=a}^{b}{\mathrm e}^{2kn}=\sum_{n=a}^{b}\left({\mathrm e}^{2k}\right)^n=\dots$ ​ $\sum_{n=a}^{b}{\mathrm e}^{2kn}=\sum_{n=a}^{b}\left({\mathrm e}^{2k}\right)^n=\dots$ ​
 +
 we get we get
  
 $\sum_{n=a}^{b}\sin(2kn)=\dfrac{\sin (k (a-b-1)) \sin (k (a+b))} {\sin(k)}$ $\sum_{n=a}^{b}\sin(2kn)=\dfrac{\sin (k (a-b-1)) \sin (k (a+b))} {\sin(k)}$
 +
 +  * The following is kinda odd:
 +<​code>​
 +Integrate[Sin[a*x]*Sin[b*x]/​x^2,​{x,​0,​Infinity}]
 +</​code>​
  
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