I'd like to define Christoffel symbols, which have three indexes. The lower indexes are symmetric. I know that it is possible to define a symmetric fonction f with
but how to define a function G[x,y,z] with only y and z symmetric, that is G[x,y,z] = G[x,z,y]?
In fact, if I enter
G[x_, y_, z_] := h[x, f[y, z]];
then G[1, 2, 3] and G[1, 3, 2] yield both h[1, f[2, 3]] but if I define a value for G[1, 2, 3] then G[1, 3, 2] doesnt yield this value? So anyone knows the trick?