ported my path-invariant stuff to Mma, after a week of arguing over how to think about it. At bedtime, (actually, long past), Julian casually tossed off an identity of the form trigamma(n0) = three contiguous pFp-1[1/4] . So I did FullSimplify[%/.n0->1/2] and went home. It's still running. Mma turned just one of the pFp-1 into a screenful of radicals and trigs of logs and arccoths, and wishes to wallow in it for eternity. Macsyma says it's equivalent to sum((((12 * j^2 + 30 * j + 19) * (2 * j + 1)!)/((j + 1) * (2 * j + 3) * 4^j * (2 * j + 5/2)!)),j,0,inf) = 2 * %pi^(3/2) - 16/(sqrt(%pi)) but when asked for a closed form for the lhs, temporized with Is 4 - g1928 * g1941 * g1960 positive, negative, or zero? Is 4 - g12326 * g1928 * g1941 positive, negative, or zero? Is 4 - g153423 * g1928 * g1941 positive, negative, or zero? and then the trump card Is false zero or nonzero? (As Jeff Golden used to say: "It's positive. Everybody knows that.") Then ten more impudent questions. Now it's just sulking. --rwg