The third equation should be
cm,n=r^αzm,n∫0r^∫02πrg(r,θ)cosmθJm(zm,nr/r^)dθdr(∫02πcos2mθdθ)(∫0r^Jm2(zm,nr/r^))
and the fourth equation should be
dm,n=r^αzm,n∫0r^∫02πrg(r,θ)sinmθJm(zm,nr/r^)dθdr(∫02πcos2mθdθ)(∫0r^Jm2(zm,nr/r^)).
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