On Tuesday, 19 January 2016 07:56:11 UTC, Dima Pasechnik wrote:
>
> In Sage sum() is by default symbolic summation, here it just gives the
> answer in terms of the Bessel function rather than sin.
> It is a correct answer, too.
>
(see e.g. (72) in
https://books.google.co.uk/books?id=9nFDvk9yr3kC&lpg=PA493&ots=LnULcCmjdI&dq=bessel(1%2F2%2Cx)&pg=PA493#v=onepage&q=bessel(1/2,x)&f=false
)
Probably the underlying engine (maxima) does not know how to simplify this
> further.
>
>
> On Tuesday, 19 January 2016 02:35:59 UTC, 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.
>>
>> Thank you!
>>
>>
>>
>>
>>
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