- #1
von_biber
- 5
- 0
need some assistance with the following integral:
\int_0^{2\pi} cosx/(a-cosx), a-parameter (say a>0)
i've converted it into a complex contour integral over z=e^(ix):
~ \int_{|z|=1} dz (z^2+1)/[z(z^2-2az+1)]
which is easily evaluated for a>1. my question regards a<1 - i am not sure how to solve it in this case, because the the 2 poles
z_1=a+Sqrt[a^2-1], z_2=a-Sqrt[a^2-1]
are exactly on the unit circle and off the real axis. thanks for any suggestions!
\int_0^{2\pi} cosx/(a-cosx), a-parameter (say a>0)
i've converted it into a complex contour integral over z=e^(ix):
~ \int_{|z|=1} dz (z^2+1)/[z(z^2-2az+1)]
which is easily evaluated for a>1. my question regards a<1 - i am not sure how to solve it in this case, because the the 2 poles
z_1=a+Sqrt[a^2-1], z_2=a-Sqrt[a^2-1]
are exactly on the unit circle and off the real axis. thanks for any suggestions!