Re: Bessel Functions

[Andreas Enge <andreas.enge@inria.fr>]

Hello,

On Wed, Aug 03, 2011 at 03:56:54PM +0000, McLaughlin, James wrote:
> Is there an implementation of the Bessel function of the first kind, I_n(z),  in Pari/gp?

Try typing
bessel
then twice the tabulator key in Gp. This will show you all function names starting
with "bessel". You are probably looking for besseli.

> Also, how do I convert a rational function to a power series of arbitrarily high degree?
> taylor(1/(1-x),x), for example,  returns
> 1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12
>  + x^13 + x^14 + x^15 + O(x^16)
> 
> How can I get an expansion up to, say, x^500?

Typing
??taylor
in Gp provides the answer: There is an optional third parameter for the series
precision.
taylor(1/(1-x),x,500)

Andreas