McLaughlin, James on Wed, 03 Aug 2011 19:11:46 +0200

 RE: Bessel Functions

```Thanks for information about the Bessel functions - besseli it is.

(However, typing bessel then twice the tab key does not do anything)

I tried your suggestion of an extra parameter in the taylor command previously, but it did not work.

I just installed
GP/PARI CALCULATOR Version 2.3.4 (released)
in case there was a problem with an earlier version but the problem is still there.

Also none of the ?? or ??? commands work.
Here is some output:

(12:53) gp > ?taylor
taylor(x,y): taylor expansion of x with respect to the main variable of y.

(12:54) gp > ??taylor
***   [pipe:] 'C:/Program\ Files/PARI/perl.exe C:/Program\ Files/PARI/gphelp -
cu 6 -fromgp  'taylor@3'' failed.
(12:55) gp > taylor(1/(1-x),x,500)
***   expected character: ')' instead of: taylor(1/(1-x),x,500)
^-----
________________________________________
From: Andreas Enge [andreas.enge@inria.fr]
Sent: Wednesday, August 03, 2011 12:36 PM
To: pari-users@list.cr.yp.to
Subject: Re: Bessel Functions

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

```