- #1
zetafunction
- 391
- 0
how could or should we consider the function
[tex] f(s)=0^{-s} [/tex] for values of 's' ??
if Re (s) is smaller than 0 then [tex]f(s)=0 [/tex]
but if Re (s) is bigger than 0 then [tex] f(s)= \infty [/tex]
If s=0 as a limite then [tex]f(0)=0^{0}=1 [/tex]
f(s) can be considered (plus a minus or + sign) as the Mellin transform [tex]f(s)=\int_{0}^{\infty}dxx^{s-1} [/tex]
if we imposed certain symmetry or regularization conditions so [tex] f(s)=f(1-s) [/tex] we would have the 'regularized' value 0 ,
then what value should i take for f(s) for every value of 's' ?
[tex] f(s)=0^{-s} [/tex] for values of 's' ??
if Re (s) is smaller than 0 then [tex]f(s)=0 [/tex]
but if Re (s) is bigger than 0 then [tex] f(s)= \infty [/tex]
If s=0 as a limite then [tex]f(0)=0^{0}=1 [/tex]
f(s) can be considered (plus a minus or + sign) as the Mellin transform [tex]f(s)=\int_{0}^{\infty}dxx^{s-1} [/tex]
if we imposed certain symmetry or regularization conditions so [tex] f(s)=f(1-s) [/tex] we would have the 'regularized' value 0 ,
then what value should i take for f(s) for every value of 's' ?