You might want to check out PARI and the wonderful Math::Pari perl wrapper, which lives on CPAN and optionally installs PARI for you.

Here's a quick example run in the gp calculator: 

? taylor(exp(y),y)
%366 = 1 + y + 1/2*y^2 + 1/6*y^3 + 1/24*y^4 + 1/120*y^5 + 1/720*y^6 + 
+1/5040*y^7 + 1/40320*y^8 + 1/362880*y^9 + 1/3628800*y^10 + 1/39916800
+*y^11 + 1/479001600*y^12 + 1/6227020800*y^13 + 1/87178291200*y^14 + 1
+/1307674368000*y^15 + O(y^16)

? taylor(sin(y),y)
%374 = y - 1/6*y^3 + 1/120*y^5 - 1/5040*y^7 + 1/362880*y^9 - 1/3991680
+0*y^11 + 1/6227020800*y^13 - 1/1307674368000*y^15 + O(y^16)

? taylor(exp(y),y)+taylor(sin(y),y)
%375 = 1 + 2*y + 1/2*y^2 + 1/24*y^4 + 1/60*y^5 + 1/720*y^6 + 1/40320*y
+^8 + 1/181440*y^9 + 1/3628800*y^10 + 1/479001600*y^12 + 1/3113510400*
+y^13 + 1/87178291200*y^14 + O(y^16)

[download]

In reply to Re: Power series computations by rhesa
in thread Power series computations by pm5

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.