Could be tetration if this integral converges

[tommy1729]

I'm curious: how did you get that first formula? Is it possible to get a similar formula for

I'm indisposed at the moment but the formula is derived in the paper I posted. Its a very brief proof and follows from cauchy's residue theorem and a meromorphic representation of the Gamma function. I could write some of it out, but it wouldn't be completely formal and might not leave you convinced .

Contour integration, right?

I could be wrong but I think James also uses Nörlund-Rice integral and Ramanujan's master theorem.
Perhaps not used literally but only in the back of his mind.

regards

tommy1729

[JmsNxn]

I could be wrong but I think James also uses Nörlund-Rice integral and Ramanujan's master theorem.
Perhaps not used literally but only in the back of his mind.

regards

tommy1729

Wow. Never seen these results before ^_^. I actually reproved ramanujan's master theorem!Not very hard the way I did it. I am using something very close to the Norlund rice integral, slightly modified though.