One way to find dI would be from lnI/I=pi/2.Assuming pi/2 constant for time being, we get:
d(lnI/I)=0
dI/(I^3)-lnI/I^2=0
dI = IlnI = -(lnI)/I = ln (I^I)=-ln(I^(1/I)= -pi/2 so that if
-I= h(I^(1/I)), dI = -ln(I^(1/I)).
so we can have
-IdI = -W(- ln(I^(1/I)) = I*(Pi/2)
IdI= W(-ln(I^(1/I))= -I*(pi/2)
We can integrate dI , IdI , etc over all hyperdimensions or finite interval of and get some values. First impression is that pi is not a constant moving from one hyperdimension to next, otherwise we get non-identities, but this have to be little experimented with.
And so on. More later.
d(lnI/I)=0
dI/(I^3)-lnI/I^2=0
dI = IlnI = -(lnI)/I = ln (I^I)=-ln(I^(1/I)= -pi/2 so that if
-I= h(I^(1/I)), dI = -ln(I^(1/I)).
so we can have
-IdI = -W(- ln(I^(1/I)) = I*(Pi/2)
IdI= W(-ln(I^(1/I))= -I*(pi/2)
We can integrate dI , IdI , etc over all hyperdimensions or finite interval of and get some values. First impression is that pi is not a constant moving from one hyperdimension to next, otherwise we get non-identities, but this have to be little experimented with.
And so on. More later.