came up with this cute lil guy in the comments of a previous thread.. Thought it deserved its own tweetpic.twitter.com/tCL4x65MxY
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Asking myself and the audience: If this integral identity implies a generalization of good old Nicomachus? Where the summation goes from 1 to p: (The case n=1, k=1 and n=2, k=1 are trivial and the case n=1, k=2 yields the identity of Nicomachus. What about k>1? k, n natural).pic.twitter.com/Uf5RcojWPH
I was thinking that exact same thing!!! let me know if you come up with something!
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I am lazy now, guess "no" one can find IMHO an easy counter example and if this is the case it fails showing how careful one must be by applying apparent/obviuos analogue-like methods But this is also how science works. Always stay critical challenge yourself and others and check
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For n=2, k=2 it is a simple counterexample for summation of p from 1 to 2: (One can also old fashioned look up the series in e.g. Jolley or: Abramowitz & Stegun).pic.twitter.com/x76FvmhwLJ
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