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