Hmm... does this mean that it might still be useable with tetration? It seems to suggest an approach reminiscent of Kouznetsov's Cauchy-integral thing but with a different integral.
Also, has anyone tried the Euler-MacLaurin sum/integral formula?
http://en.wikipedia.org/wiki/Euler%E2%80...in_formula
http://mathworld.wolfram.com/Euler-Macla...mulas.html
These seem to be able to construct pure differential equations, or integral/differential equations, albeit of infinite order, for tetration. Just replace the continuous sum in the tetration sum formula with the given integral/differential expression. This gives an integral/differential equation that also references the values of the function and derivatives at point 0. Then one can differentiate both sides and one has a pure differential equation of infinite order.
Could that be useful?
Also, has anyone tried the Euler-MacLaurin sum/integral formula?
http://en.wikipedia.org/wiki/Euler%E2%80...in_formula
http://mathworld.wolfram.com/Euler-Macla...mulas.html
These seem to be able to construct pure differential equations, or integral/differential equations, albeit of infinite order, for tetration. Just replace the continuous sum in the tetration sum formula with the given integral/differential expression. This gives an integral/differential equation that also references the values of the function and derivatives at point 0. Then one can differentiate both sides and one has a pure differential equation of infinite order.
Could that be useful?