Complex Exponential: What is e^jw∞?

[tommyhakinen]

what is e$$^{jw\infty}$$ ?

 

[WWGD]

You cannot define it in the complex plane, since oo is not a complex number. You may

want to work on the Riemann sphere, or something, if you want to work with the log,

tho I don't see how to do so at this point. e^z must be defined in terms of a branch

of logz , to be well-defined, in the sense of being single-valued, among other things.

Since logz is not even defined in the whole complex plane, you cannot define a logz

to be analytic in the extended complex plane