06/26/2008, 07:16 PM
However as I now see the Hadamard and Luschny definitions hava a major drawback, they dont satisfy
\( (x+1)!=(x+1)x! \)
they merely interpolate n!. So there is no (mentioned) alternative definition of the gamma function that satisfies the above equation.
For tetration we too demand that
\( b[4](x+1)=b^{b[4]x} \)
and that it is not just an interpolation for b[4]n.
However here there seem to be several competing definitions.
\( (x+1)!=(x+1)x! \)
they merely interpolate n!. So there is no (mentioned) alternative definition of the gamma function that satisfies the above equation.
For tetration we too demand that
\( b[4](x+1)=b^{b[4]x} \)
and that it is not just an interpolation for b[4]n.
However here there seem to be several competing definitions.