Taylor and Laurent Series
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Complex Analysis › Taylor and Laurent Series
Questions 1 - 2
1
Find the Taylor Series expansion of
Explanation
It is well known (can be shown by the definition) that that
Making the appropriate substitutions
Shifting the index of summation gives us
2
Find the first three terms of the Taylor Series of
Explanation
Taylor Series expansion of the numerator and the denominator seperately gives us
A term by term multiplication gives us
Combining like terms