ramanujan and tetration  Printable Version + Tetration Forum (https://math.eretrandre.org/tetrationforum) + Forum: Tetration and Related Topics (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1) + Forum: Mathematical and General Discussion (https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3) + Thread: ramanujan and tetration (/showthread.php?tid=169) Pages:
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Thats not tetration!  bo198214  05/30/2008 galathaea Wrote: I was really curious how Ramanujan's continuous iteration of would look like. But now I am a bit disappointed. What he considers is not iterated but iterated ! Not that this would be entirely trivial, however this is a case where the function to iterate has a fixed point at 0 and there is only one way to obtain (continuous/fractional/real/complex/analytic) iterates of the formal powerseries and that is regular iteration. So, though its amazing that he considered the topic of regular iteration at such an early time, he does not contribute towards analytic tetration, where the difficulty is exactly this . RE: ramanujan and tetration  Ivars  05/30/2008 galathaea Wrote:in the formal setting Thanks galathaea for answer to my musings and further development. I am interested in tetration ( and further) because it is the next obvisously integer order of infinity. If rules and analogies for discrete enumerable by some integers orders of infinity can be established, than later it should be possible to cover all intermediate ranges by extensions to fractional and rational and real and complex change of orders of infinity as usually. So I am looking to start with integers that enumerate these discrete orders of infinity and then look back into what is between exponentiation and tetration if needed. I was trying to link it to combinatorics of branching tree chains but can not find any basic text about this subject to even understand the conventions people working in them use. One thought about trees is that divergent series most likely end up in different (almost?) continuous orders of infinity via tree type ( bifurcation, trifurcation, n furcation etc) structure. The correspondance between a type of series and order of infinity ? Ivars 