Fwd: Stepen Lucas's "Integral approximations to Pi with nonnegative integrands"

Seems like it would be straightforward to translate to Maxima
the Maple program shown in the referenced paper.
CVS Maxima seems to be able to compute the integrals
(5.17.1 asks about the sign of parameters).
The "type" stuff seems to be a set membership or maybe just
a pattern-matching test; maybe freeof could replace it.
Haven't looked at the paper in any detail. Have fun!

Robert Dodier


---------- Forwarded message ----------
From: "Alexander R.Povolotsky" <apovo... at gmail.com>
Date: Feb 19, 5:49 pm
Subject: Stepen Lucas's "Integral approximations to Pi with
nonnegative integrands"
To: sci.math.symbolic


Hi,

S. K. Lukas in

http://www.math.jmu.edu/~lucassk/Papers/more%20on%20pi.pdf<http://www.math.jmu.edu/%7Elucassk/Papers/more%20on%20pi.pdf>;

derived several identities, which relate Pi (via definite integrals)
with
the several few Pi fractional convergents, which denominators and
numerators
are described in

http://www.research.att.com/~njas/sequences/A002486<http://www.research.att.com/%7Enjas/sequences/A0024865>http://www.research.att.com/~njas/sequences/A002485<http://www.research.att.com/%7Enjas/sequences/A0024865>;

I raised the issue re the possibility of deriving generalized ("n"
parameter
based ) definite integral identity relating Pi with ALL (each at its
own
value of n) Pi fractional convergents (referenced in above sequences)
- see my exchange with S. K. Lukas below.

  Unfortunately I do not have sufficient computational resources (I do
not have access to Maple or Mathematica, instead I have Pari/GP
installed
on my very old home computer) to take advantage of Stephen's generous
offer to play with his Maple program, which he wrote and which is
listed in

 http://www.math.jmu.edu/~lucassk/Papers/more%20on%20pi.pdf<http://www.math.jmu.edu/%7Elucassk/Papers/more%20on%20pi.pdf>;

The program is on page 9 of the linked to pdf and
that it is literally only 18 lines of code.
May one of you could help me running
Stephen's program towards experimental attempt of deriving desired
generalized
identity?

Thanks,
Best Regards,
Alexander R. Povolotsky