Abstract

proof, `Although this proof is not very long, it seems too complicated compared with the elegance of the statement. It would be nice to find a more natural proof': Unfortunately much the same can be said of the proof that I have presented here. Markett [7] and J. Borwein and Girgensohn [3] were able to evaluate i(p 1 ; p 2 ; p 3 ) in terms of values of i(p) whenever p 1 + p 2 + p 3 6, and in terms of i(p) and i(a; b) whenever p 1 + p 2 + p 3 10 --- it would be interesting to know whether such `descents' are always possible or, as most researchers seem to believe, that there is only a small class of such sums that can be so evaluated. Proof of (1).

Citations