>> Axiom has a closed form for 2 integrals where Schaums has series. > >But at least one of them seems to be wrong. Since it seems that my message was >overlooked, I repeat it here: > >[EMAIL PROTECTED] writes: > >> 14:668 SCHAUMS AND AXIOM DIFFER (Axiom has closed form) > >But I'm not so sure that it is correct, at least not for a=1 and x in 0..1. > >draw(D(integrate(asech(x)/x,x),x)-asech(x)/x, x=0..1) > >I'm an absolute nobody on this stuff, so I may well be missing something. On >the other hand, the power series for (asech x)/x + (log x - log 2)/x is >Dfinite: > >(76) -> guessPRec [coefficient(series normalize((asech x + log x - log 2) / >x)::GSERIES(EXPR INT, x, 0), i) for i in 0..30] > > (76) > [ > [ > function = > BRACKET > f(n): > 2 2 1 > (n + 6n + 9)f(n + 2) + (- n - 3n - 2)f(n)= 0,f(0)= 0,f(1)= - - > 4 > , > order= 0] > ] > Type: List Record(function: Expression Integer,order: NonNegativeInteger) > >and this doesn't agree at all with the power series you get from >D(integrate(asech(x)/x,x),x). > >Should be investigated,
Martin, I saw your note but haven't yet had the time to prove the result one way or the other. I just finished the last integrals and did a bug-catching, "check my homework" review last night. I plan to use the 3 Ms to check both Axiom and Schaums. Ultimately, I suspect they are both "right" under some as-yet-unstated set of assumptions. But I have much more to learn about branch cuts, which ones are assumed, and how they propagate before I think I have a solid clue. These assumptions should really be written down someplace but they are not. Tim _______________________________________________ Axiom-developer mailing list Axiom-developer@nongnu.org http://lists.nongnu.org/mailman/listinfo/axiom-developer
