I want to calculate <mrow class="MJX-TeXAtom-ORD"> <mtext>Res</mtext> </mrow>

Felix Moore

Felix Moore

Answered question

2022-06-04

I want to calculate Res 2 z 2 e 1 z 2

Answer & Explanation

Xavier Vargas

Xavier Vargas

Beginner2022-06-05Added 4 answers

You are calculating the residue at z = 2 . So you need the coeff of 1 z 2
You have z 2 = ( z 2 ) 2 + 4 z 4 = ( z 2 ) 2 + 4 ( z 2 ) + 4
Using this you get
z 2 n = 0 1 n ! ( z 2 ) n = n = 0 ( z 2 ) 2 + 4 ( z 2 ) + 4 n ! ( z 2 ) n
So the Residue(Coeff of 1 z 2 ) is :-
1 3 ! + 4 1 2 ! + 4 1 1 ! = 1 6 + 6

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