Residue of [cosh (1/0)]^2

I need to find the residue at z = pi of:

f(z)=\left[\cosh\left(\dfrac{1}{z-\pi}\right)\right]^2

I think I first need to find the order of the pole (2?) but the only way I know of doing that is doing

f(z)(z-\pi)^N

, which doesn't seem to work with the cosh...

Reply 1

marcusmerehay

17

You may well need to consider the Taylor/Laurent Series of

f(z)

around

z=\pi

in this example.

If you're not confident in doing it, Wikipedia has a semi-decent worked example. (I've not done any complex analysis for 18 months, so it would take a while for me to refresh my memory :colondollar:

)

Reply 2

Zygroth

OP

14

Original post by marcusmerehay

You may well need to consider the Taylor/Laurent Series of

f(z)

around

z=\pi

in this example.

If you're not confident in doing it, Wikipedia has a semi-decent worked example. (I've not done any complex analysis for 18 months, so it would take a while for me to refresh my memory :colondollar:

)

Oh yeah I can use the expansion for cosh...

Residue of [cosh (1/0)]^2

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