Log[(z+5)/(z^2+3z+2)] How is this analytic on the real segment

factor z^2+3z+2 brainlet

also there's a stupid question thread

>>8793602

Roots are z=-1 and z=-2, so not analytical on there. I'm asking about the interval (-2,-1).

The argument for

Log[(z+5)/(z^2+3z+2)]

is negative on that segment. Can it still somehow be analytical or is the book wrong?

>>8793600
because you can expand it as a power series locally at all points obviously

use another branch

>>8793730

How does it differ from the case x ≤ -5, y = 0? Book claims non-analyticity there as well.

>>8794097
i don't understand the issue

a function is analytic on a strip on the real line if it is analytic in a neighborhood of that strip in the complex plane.

there is no way to define the complex logarithm at zero, however there is always a way to define the complex logarithm on any SIMPLY CONNECTED subset of the complex plane minus zero. so you have to make a branch cut, usually on the positive or negative real line

if you want to take the logarithm of a function, you look at the range of that function

the rational function (z+5)/((z+2)(z+1)) has critical values at -5, -2, and -1. on (-2,-1) the range of the function is strictly negative real numbers, so you can define a logarithm there. same thing when z<-5, although when z = 5 then there is an issue.

>>8793600
Why is there no holomorphic function on the unit disk with f(1/n)=2^(-n) n=2,3... ?

>>8793600
that guy's face is full of stupidity just look at him he looks like a cretin he looks like a gaping Anoos

>>8794785
>hahah le funny face haha funny look hahaha
kill yourself

>>8794923
>le kill yourself meme
too stupid and unoriginal to come up with your own insult? I shit on your brain you stupid brainlet

i shit on your soul

>>8794771
take your domain as the unit disk minus zero. this function is identical to 2^(-1/z) on 1/n for n=2,3,...

call the function f. then f(z) - 2^(-1/z) has zeros at these points. if zero is a pole then z^n(f(z) - 2(-1/z)) has a removable singularity for some large enough n and so it is the zero function because zero is an accumulation points of zero.

if f(z)-2^(-1/z) does not have a pole then it has an essential singularity.

hopefully you get an idea that either way f(z) cannot be extended to the whole disk.

>>8794958
>complain about original insults
>HAHAHAHA BRAINLET
And besides, it was a suggestion, not an insult.

>>8794973
you're hilarious man I am so happy knowing that people as stupid as you exist on this planet thanks to capitalism and competition between humans i will shit on your life and take all your resources i will become rich and optimized while you become poorer and poorer

>>8794979
Of course you will. Like Mcduck.

A children tale, a fantasy. Good luck.

>>8794992
I'm already at a top 10 university I piss on your life brudda, whenever I piss you come to the toilet and open your mouth thinking that if you catch a droplet of piss you may increase your IQ by a few decimals