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To Martin (cliclic...@freenet.de
Posted:
Aug 15, 2010 9:02 PM


Dear Martin,
In 2009 based on results obtained by Stephen Lucas's "Integral approximations to Pi with nonnegative integrands" I made the following generalizing conjecture ===================================================== There are exists some integer functions of n, namely i(n), k(n), l(n) and m(n) , where i(n) function appears to represent the various powers of 2, while l(n) is an integer, which is power 2 factor free (except for trivial power of 0)
such so there exists general integral identity (using Maple's notation)
Pi= A002485(n)/A002486(n)1/(i*l)*Int(x^m*(1x)^m*(k+(k+l)*x^2)/ (1+x^2),x = 0..1) =============================================================== I was able to confirm above for nontrivial cases of n=2, 3, 4, 5, 6 but don't have computational resources to check whether my conjecture stays true for n>6 I wrote in 2009 to S. Lucas asking for help but he was not interested and suggested that I pursue it on my own.
Could Derive help to solve my problem ?
Thanks, Best Regards, Alexander R. Povolotsky



