Or so I thought. Rich showed me http://arxiv.org/abs/1010.1420 which sez (p 15) "Taking the even part of the continued fraction (corresponding to the 2n-th convergents) on the right-hand side of (37) gives ..." I never heard of "the even part of a continued fraction", but what they mean is to pairwise coalesce terms, which does not obviously produce another C.F. without a slightly tricky maneuver (http://gosper.org/stanfordn2.pdf), with which you can convert to a C.F. any composition of homographic transformations. E.g., pairwise grouping the "period 2" C.F. for e^z in DLMF 4.9.3b (A&S 4.2.40(b)), 2 2 (2 n + 3) z 2 (- z + 4 (n + 1) - 1) exp z = 1 + z + K (------------ // ------------------------), n>=0 2 n + 1 2 n + 1 k terms of which give the Pade(k+1,k). --rwg