09/23/2013, 11:18 PM
I was thinking about some " intresting " functions.
Not sure how to define " intresting " though.
For example :
exp(a+bi) = a+bi
f(z) = ln( (exp(z) - z) / (z^2 + 2az + a^2 + b^2) )
Where a and b are real and z is complex.
It seems f(z) must be entire since exp(z) has only 2 fixpoints.
Another example is
f(z) = ln( (2sinh(z) - z) / z )
Forgive me for once again writing 2sinh(z)
Im a 2sinholic
We can get Taylor series for these kind of functions.
But I wonder if these have been studied before ?
They appear both "elementary and exotic " to me.
regards
tommy1729
Not sure how to define " intresting " though.
For example :
exp(a+bi) = a+bi
f(z) = ln( (exp(z) - z) / (z^2 + 2az + a^2 + b^2) )
Where a and b are real and z is complex.
It seems f(z) must be entire since exp(z) has only 2 fixpoints.
Another example is
f(z) = ln( (2sinh(z) - z) / z )
Forgive me for once again writing 2sinh(z)
Im a 2sinholic
We can get Taylor series for these kind of functions.
But I wonder if these have been studied before ?
They appear both "elementary and exotic " to me.
regards
tommy1729