[math-fun] outlandish 2F1[4/5]

Hypergeometric2F1[1/8, 5/8, 3/4, 4/5] == (Pi*((Sqrt[1 + Sqrt[5]]*(10*(1 + Sqrt[5])*Pi + Sqrt[5]*Log[5] + 5*Log[9 - 4*Sqrt[5]]))/ (Gamma[11/20]*Gamma[19/20]) - (Sqrt[5 - Sqrt[5]]*(2*(-5 + 3*Sqrt[5])*Pi + Sqrt[5]*Log[5] + 5*Log[9 - 4*Sqrt[5]]))/ (Gamma[13/20]*Gamma[17/20])))/(20*Gamma[1/4]^2) Mma 8.04 knows squat about 2F1[4/5]. Macsyma knows most, but divides by 0 here. But it could take the requisite limit, which Mma couldn't. But Macsyma couldn't simplify it, which Mma could. (You can never have too many CASes.) DLMF 15.4iii just quotes A&S and still doesn't even know the 2F1[1/5]s. (And rejected my services, back in the day.) --rwg