1
$\begingroup$

Let $f$ an analytic function of complex variable, with radius of convergence $r$. What about the radius of $x^pf(x),$where $p$ is a complex parameter ?

Thanks in advance

  • 0
    the conter is the origin2012-12-11

1 Answers 1

2

(I assume you mean convergence radius around $x=0$.) This function is only single valued around $x = 0$ if $p \in \mathbb{Z}$. It extends over $x=0$ only if $p \in \mathbb{N}$ in which case its radius of converge is the same as that of $f(x)$.