Let be a function of a complex variable, defined over a domain in . We write , where and are real numbers, i.e. is written in algebraic form. We can write in algebraic form too, i.e.

Thus

and |

Conversely, if we have a function given in algebraic form (v.s. 3)

we can compute a ``closed'' form for , using the following remark:

Of course, the converse process is possible, i.e. for a function given by a formula like , Euler formulas can be used to give an expression in and for .

Thus,

Noah Dana-Picard 2007-12-24