Just an observation (and no conclusions :-(
(C1) taylor(rat(sum(x^k*sum(i^k,i,1,d),k,0,inf)),x,0,1),simpsum;
2
(d + d) x
(D1)/T/ d + ---------- + . . .
2
(C2) ?genvar;
(D2) (d8001, 'SUM(('SUM(i^k,i,1,d))*x^k,k,0,INF)8000,
'SUM(('SUM(i^k,i,1,d))*x^k,k,0,INF)7999)
Here is your bug (in case you forgot ;-)
(C3) taylor(sum(x^k*sum(i^k,i,1,d),k,0,inf),x,0,1),simpsum;
2
(i + i) x
(D3)/T/ i + ---------- + . . .
2
(C4) ?genvar;
(D4) (i8107, d8082, d8001, 'SUM(('SUM(i^k,i,1,d))*x^k,k,0,INF)8000,
'SUM(('SUM(i^k,i,1,d))*x^k,k,0,INF)7999)
(C5)
Sorry if you have already come across this thing. Apparently, in the
(correct) first case, the double sum is encapsulated in such a way
that GENVAR does not even contain a gensym corresponding to i (as an
inspection of the property lists of the elements of GENVAR confirms).
Wolfgang