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HypergeometricPFQ - simplification

• To: mathgroup at smc.vnet.net
• Subject: [mg89153] HypergeometricPFQ - simplification
• From: janos <janostothmeister at gmail.com>
• Date: Tue, 27 May 2008 07:15:11 -0400 (EDT)

Could anyone show using Mathematica that the expression

-2/27 + (253*HypergeometricPFQ[{-1/2, -1/6, 1/6}, {4/3, 5/3}, -1/729])/
108 - (911*HypergeometricPFQ[{1/2, 5/6, 7/6}, {7/3, 8/3}, -1/729])/
6298560 +
 (73*HypergeometricPFQ[{3/2, 11/6, 13/6}, {10/3, 11/3}, -1/729])/
9795520512

is equal to

(-2*(-1 + 10*Sqrt[10]))/27? (Using, say, TraceInternal, to see what is
going on.)

Thank you,

Janos