[math-fun] elliptic mean

Wrt Means, Gosper's objection was a bit more subtle: should we require that

avg( avg(a,b), avg(c,d) ) = same thing with b and c swapped? Bingo. "Association" was a poor choice of words. Dyadic symmetry?

This *is* true for ordinary averages, and geometric, harmonic, etc. means. And the resulting symmetric expressions make it obvious how to define avg(a,b,c). A nonobvious def in terms of dyadic avg is the root of

avg(avg(a,b),avg(c,x)) = x . This does *not* work with elliptic mean. One plausible def is to iterate [a,b,c] <- [em(b,c),em(c,a),em(a,b)]. But I think em should be classified among the unscrupulous means. --rwg