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From: rancid moth on 24 May 2010 21:10
I'm having difficulty determining the behaviour of the singularities for
this function:

F(z) = sin(y*x)/(z-y^2) - sin(x*sqrt(z))*sin(y*g(z))/{
(z-y^2)*sin(sqrt(z)*g(z))}

where g(z) = 2/z + 1/(z^2-1)

i know z=y^2 is a removable singularity. I _think_ that if z=z_n
represents the solution of sqrt(z)*g(z)=n*pi, then the residues of F(z) at
the z_n are

(-1)^(n+1)*sin(y*n*pi/sqrt(z_n))*sin(x*sqrt(z_n))/(z_n-y^2)

but what of the z_n, and how do they behave in the complex plane? i
believe they satisfy a quintic, and that as n->oo z_n--> -1,0,1, of which
i think only 0 is an essential singularity of F(z)...perhaps.
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