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Mathematik-Online problems:

Problem 106: Division of Power Series

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Find the first four elements of the power series expansion of the given functions:
a) $ {\displaystyle{f(z)=\frac{\sin z}{\cos z}}}$ b) $ {\displaystyle{f(z)=\frac{z}{{\rm {e}}^z}}}$ c) $ {\displaystyle{f(z)=\frac{1}{z^2+3z+1}}}$
Hint: Multiply the equation $ {\displaystyle{f(z)=\frac{\sum a_nz^n}{\sum b_nz^n}}} =: \sum c_nz^n$ by $ \sum b_nz^n$ and determine the factors $ c_n$ by comparing the coefficients.

(Authors: Apprich/Höfert)

see also:

[Solutions]
  automatisch erstellt am 14. 10. 2004