On Monday, January 18, 2016 at 6:35:59 PM UTC-8, saad khalid wrote:
>
> Hello everyone:
>
> I'm trying to compare some functionality in Sage with that of Mathematica.
> For my assignment, I have to take this series:
>
> sum((-1)^n*((x)^(2*n+1))/factorial(2*n+1),n,0,oo)
>
>
> And put it into a mathematical software to see what function it is
> equivalent to. In this case, this series is supposed to be equivalent to
> the sine function. Indeed, when I put the following code in Mathematica, it
> says that it is the Sine function:
> Sum((-1)^n*((x)^(2*n+1))/((2*n+1)!),{n,0,Infinity})
>
> I was hoping that there would be something similar to this in Sage. I'm
> trying to symbolically use the sum function with the following code:
>
> x = var("x")
> n = var("n")
> k = var("k")
> show(sum(((-1)^n)*((x)^(2*n+1))/factorial(2*n+1),n,0,oo))
>
> What it outputs is not the sine function. Instead, it says that it is
> equivalent to:
>
> 1/2*sqrt(2)*sqrt(pi)*sqrt(x)*bessel_J(1/2, x)
>
>
> I don't know why exactly it says this but I was wondering if there was any
> way for Sage to do what Mathematica is doing here, in recognizing the
> popular series and outputting that when I try to symbolically evaluate this
> sum.
>
>
As Dima mentions, the relevant functionality is coming from Maxima in this
case. Maxima does have a flag you can set to let it try to expand bessel
functions into elementary functions, see
http://maxima.sourceforge.net/docs/manual/maxima_15.html#SEC80
It's not directly exposed in sage, but with some obscure code you can
activate it:
sage: maxima_calculus("besselexpand:true")
true
sage: sum(((-1)^n)*((x)^(2*n+1))/factorial(2*n+1),n,0,oo)
sin(x)
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