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 [2014] Beyond Gamma and Barnes-G tommy1729 Ultimate Fellow Posts: 1,370 Threads: 335 Joined: Feb 2009 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 « Next Oldest | Next Newest »

 Messages In This Thread [2014] Beyond Gamma and Barnes-G - by tommy1729 - 12/28/2014, 05:04 PM RE: [2014] Beyond Gamma and Barnes-G - by MphLee - 12/28/2014, 05:48 PM

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