1 Apr
2014
1 Apr
'14
2:15 a.m.
I set about collecting a toolbox of identities relating (n/d)! to <pile of (p/q)!, with q<d, or failing that, (p/d)! with p<n >, in hopes of discerning a pattern. (3/14)! == (7 2^(3/7) Cos[\[Pi]/7]^(9/7) (2/7)! (3/7)! Sin[\[Pi]/7] (Sin[\[Pi]/14] Sin[(3 \[Pi])/14])^(2/7))/Sqrt[\[Pi]] per LatticeReduce, but presumably also from finite massage by the tuplication and reflection formulæ. Uh huh. --rwg Caution: Federal Law prohibits ... almost everything.