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.
Thank you!
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