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+--- Thread: Could be tetration if this integral converges (/showthread.php?tid=847)
RE: Could be tetration if this integral converges - tommy1729 - 05/12/2014
(05/12/2014, 02:15 AM)mike3 Wrote:(05/12/2014, 01:44 AM)JmsNxn Wrote:(05/11/2014, 11:26 PM)mike3 Wrote: 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
RE: Could be tetration if this integral converges - JmsNxn - 05/13/2014
(05/12/2014, 11:26 PM)tommy1729 Wrote: 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.