Title: A "forgotten" theorem about complex numbers Post by: hgjf2 on July 18, 2013, 09:27:07 AM If giving a function f:C->C where C is complex numbers set, and f(z)=f(z+k+l*i) where k,l<-R (real numbers) and z=a+bi.
Exist least on complex number z0 for f(z0) = 1/0 (infinity) Title: Re: A "forgotten" theorem about complex numbers Post by: Roquen on July 18, 2013, 10:54:33 AM I'm not understanding what you're saying. You seem to be defining translation. F(z) = z+t with z,t elements of C.
Title: Re: A "forgotten" theorem about complex numbers Post by: hgjf2 on July 18, 2013, 07:51:07 PM I'm not understanding what you're saying. You seem to be defining translation. F(z) = z+t with z,t elements of C. f(z) is defined here as periodical function with two complex vectors orthogonals. Than f(z)=f(z+km+lni) like sin(z)=sin(z+2k[pi]) and exp(z)=exp(z+2ki[pi]).k,l<-Z (integers) and m,n<-R (real parameters) and i=sqrt(-1). More explains: A function like f(z) from my definition is integral(sqrt(sin(z))) as example. f(z)=f(z+m)=f(z+2*m)=... =f(z+ni)=f(z+m+ni)=f(z+2*m+ni)=... =f(z+2*ni)=f(z+m+2*ni)=f(z+2*m+2*ni)=... Title: Re: A "forgotten" theorem about complex numbers Post by: kram1032 on July 22, 2013, 04:24:32 PM So you're asking wether there always exists a complex number z0 such that f(z0) has a pole (http://en.wikipedia.org/wiki/Pole_%28complex_analysis%29)of 1-st grade at z0, given the function f is periodic in both the real and the imaginary direction? |