[math-fun] signature 3 vs signature 2

Tabulating 2F1s without symbolic parameters nor argument makes about as much sense as trying to build a bestiary with complete genomes. Unless the table is gigantic, the chance of matching your exact animal is minute. Nevertheless, you might enjoy a few closed forms, simultaneously expressed as 2F1[1/3,2/3,1,<algebraic>], Gammas, and 2F1[1/2,1/2,1,<algebraic>] = K(<algebraic>). --rwg gosper.org/sig2sig3.png (Still no luck simplifying that ridiculous expression for 2F1[1/3,2/3,1,-1].)