Take the 2-minute tour ×  Could somebody please explain what are
the differences between    1. a differentiable function and a
holomorphic function    2. analytic function and conformal
function? (Am I right to think that all analytic functions are
conformal and vice versa, but the adjectives just refer to
different characteristics of the function -- former: can be
expressed as a series, latter: preserves angles)?  Thank you.
share|improve this question add comment  1 Answer  up vote 3
down vote accepted  For a complex function defined on a domain,
"differentiable", "holomorphic" and "analytic" are equivalent,
but the words emphasize different features of the function:    •
"Differentiable" emphasizes that the function can be
differentiated (well, duh).    • "Analytic" emphasizes that the
function can be specified by power series in a neighborhood of
every point.    • "Holomorphic" emphasizes the phenomenon that
the values of the function on some small subset can determine
its values on the entire domain.  D