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## Re: [Axiom-developer] Re: About Schaums.

**From**: |
root |

**Subject**: |
Re: [Axiom-developer] Re: About Schaums. |

**Date**: |
Wed, 30 Apr 2008 17:09:35 -0400 |

>*> 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:*
>
>*address@hidden 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