Just in case you haven't seen: Shalosh B.EKHAD (Doron Zeilberger): {Forty Strange Computer-Discovered Hypergeometric Series Evaluations}, 12-October-2004. Online at \url{http://www.math.rutgers.edu/~zeilberg/pj.html}. Raimundas Vid\={u}nas: {Darboux evaluations of algebraic Gauss hypergeometric functions}, arXiv:math.CA/0504264, 13-April-2005. Online at \url{http://arxiv.org/abs/math/0504264}. For the DLMF these might be fine input: Raimundas Vid\={u}nas: {Expressions for values of the gamma function}, arXiv:math.CA/0403510, 30-March-2004. Online at \url{http://arxiv.org/abs/math/0403510}. And pretty please Garvan's two papers giving AGM iterations for F([1/2+s,1/2-s],[1],z) (and some others): J.\ Borwein, P.\ Borwein, Frank Garvan: {Hypergeometric Analogues of the Arithmetic-Geometric Mean Iteration}, Constr.\ Approx.\ 9, 1993.} %Online at \url{http://www.math.ufl.edu/fac/facmr/Garvan.html}. (disappeared) Frank Garvan: {Cubic modular identities of Ramanujan, hypergeometric functions \ and analogues of the arithmetic-geometric mean iteration}, Contemporary Mathematics 166, 1993. %Online at \url{http://www.math.ufl.edu/fac/facmr/Garvan.html}. (disappeared) * R. William Gosper <rwg@osots.com> [Nov 25. 2005 06:37]:
I said There are also similar identities for 2F1(phi^-2).
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-- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.