On Mon, Sep 28, 2020 at 04:03:48PM -0400, Fernando Q. Gouvea wrote:
> I am trying to see how to do a standard calculus exercise in Sage. I want a
> power series for the integral of sin(x)/x. I tried:
>
> sage: var('t')
> t
> sage: assume(x>0)
> sage: f(x)=integrate(sin(t)/t,t,0,x)
> sage: f
> x |--> sin_integral(x)
> sage: taylor(f(x),x,0,10)
> 73/466560*x^9 - 127/35280*x^7 + 31/600*x^5 - 7/18*x^3 + x
That's odd. I get the same behavior in sage8.9 and my current develop
branch of sage.
Annoyingly, I notice that if you get the Taylor series as you might in a
calculus class, by first getting the Taylor series and then integrating
it term by term, it comes out differently (and correctly).
var('t')
littlef(t) = taylor(sin(t)/t, t, 0, 10)
bigf(x) = integrate(littlef(t), t, 0, x)
x |--> -1/439084800*x^11 + 1/3265920*x^9 - 1/35280*x^7 + 1/600*x^5 - 1/18*x^3 +
x
I don't know why what you tried fails. This seems to be a bug.
On the trac, this seems closely related to
1. https://trac.sagemath.org/ticket/11164
2. https://trac.sagemath.org/ticket/30389
- DLD
--
David Lowry-Duda <[email protected]> <davidlowryduda.com>
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