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Topic: To Martin (cliclic...@freenet.de
Replies: 0

 apovolot@gmail.com Posts: 104 Registered: 9/4/08
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 non-negative 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*(1-x)^m*(k+(k+l)*x^2)/
(1+x^2),x
= 0..1)
===============================================================
I was able to confirm above for non-trivial 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