Computational definitions for interesting complex functions - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-20T22:06:48Z http://mathoverflow.net/feeds/question/30961 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30961/computational-definitions-for-interesting-complex-functions Computational definitions for interesting complex functions Mau 2010-07-07T21:54:00Z 2010-07-07T22:15:41Z <p>I'm after a reading source for a set of 'interesting' functions $f:\mathbb{C}^m \rightarrow \mathbb{C}$, complete with definitions that can be used to compute them numerically.</p> <p>I'm looking for functions bearing graphs with interesting (read: varied) behaviour, or that can be composed in order to generate more diverse ones.</p> <p>An example building block is the <code>exp</code> function which we can define as</p> <p>$e^{a \ + \ ib} = e^{a} \ (\cos a + i\sin b)$</p> <p>which can be immediately implemented numerically.</p> <p>Functions</p> <ul> <li>like <code>exp</code>, that can be defined in terms of real ones;</li> <li>that have some known algorithm for computing the complex components;</li> <li>that are defined in terms of others in the list,</li> </ul> <p>are good.</p> <p>Does anyone know of a 'list' of such common/interesting computable functions, from books or web (preferably)? Making it up on the spot is good too.</p> <p>Apologies for the lack of formality :) Thanks!</p>