# A very Odd function

1. Feb 25, 2010

### zetafunction

how could or should we consider the function

$$f(s)=0^{-s}$$ for values of 's' ??

if Re (s) is smaller than 0 then $$f(s)=0$$

but if Re (s) is bigger than 0 then $$f(s)= \infty$$

If s=0 as a limite then $$f(0)=0^{0}=1$$

f(s) can be considered (plus a minus or + sign) as the Mellin transform $$f(s)=\int_{0}^{\infty}dxx^{s-1}$$

if we imposed certain symmetry or regularization conditions so $$f(s)=f(1-s)$$ we would have the 'regularized' value 0 ,

then what value should i take for f(s) for every value of 's' ???