I have problem with point singularities at $\infty$. For example: Determine the nature of the point at infinity functions. For zero or pole enter times. we have function $f(z)=\frac{z-\frac{\pi}{2}}{cosz}$. So in this function we have regular point at $\frac{\pi}{2}$ times one. And I don't know how to determine this point at infity function. Can someone explain me?
Specify point singularities
0
$\begingroup$
complex-analysis
singularity-theory
singularity
-
0Why $\dfrac{\pi}{2}$ is pole.? – 2017-01-23
-
0My bad it's regular point – 2017-01-23
-
0What's the definition of a pole? – 2017-01-23
-
0@MyGlasses $z_0$ is a pole when $\lim\limits_{z->z_0}f(z)=\infty$ – 2017-01-23
-
0Well, what about your function.? – 2017-01-23
-
0@MyGlasses in point $\frac{\pi}{2}$ we have regular point but in $\frac{\pi}{2}+k\pi$ where $k\in \mathbb{Z}$ without $0$ we have pole times one – 2017-01-23
-
0Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/52310/discussion-between-myglasses-and-zxc). – 2017-01-23