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A very Odd function

  1. Feb 25, 2010 #1
    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' ???
     
  2. jcsd
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