12/28/2014, 05:04 PM

Most of you here are familiar with the Gamma function , Barnes-G function , the K-function , the double gamma function etc.

But in the spirit of my generalized distributive law / commutative assosiative hyperoperators I was wondering about

f(z+1) = f(z)^ln(z)

It makes sense afterall :

f1(z+1) = z + f1(z) leads to the triangular numbers.

f2(z+1) = z f2(z) leads to the gamma function.

f3(z+1) = f3(z)^ln(z)

Notice f_n(z) = exp^[n]( ln^[n]f_n(z) + ln^[n](z) )

So is there an integral representation for f3 ?

How does it look like ?

Analogues of Bohr-Mullerup etc ?

Hence the connection to the hyperoperators.

regards

tommy1729

But in the spirit of my generalized distributive law / commutative assosiative hyperoperators I was wondering about

f(z+1) = f(z)^ln(z)

It makes sense afterall :

f1(z+1) = z + f1(z) leads to the triangular numbers.

f2(z+1) = z f2(z) leads to the gamma function.

f3(z+1) = f3(z)^ln(z)

Notice f_n(z) = exp^[n]( ln^[n]f_n(z) + ln^[n](z) )

So is there an integral representation for f3 ?

How does it look like ?

Analogues of Bohr-Mullerup etc ?

Hence the connection to the hyperoperators.

regards

tommy1729