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Extracting terms of a polynomial into a list and then multiply each

• To: mathgroup at smc.vnet.net
• Subject: [mg90354] Extracting terms of a polynomial into a list and then multiply each
• From: Bob F <deepyogurt at gmail.com>
• Date: Mon, 7 Jul 2008 05:05:53 -0400 (EDT)

Can anyone suggest a way to extract the terms of a polynomial into a
list. For example the integral of the series expansion of

             1
    --------------------
    (1 - t^2) ^(1/2)

could be expressed in Mathematica (the first 50 terms) as

      Integrate[Normal[Series[(1 - t^2)^(-1/2), {t, 0, 50}]], {t, 0,
x}]

and gives the polynomial

    x + x^3/6 + (3 x^5)/40 + (5 x^7)/112 + (35 x^9)/1152 + (63 x^11)/
2816 + (231 x^13)/13312 + (143 x^15)/10240 +
         (6435 x^17)/557056 + (12155 x^19)/1245184 + (46189 x^21)/
5505024 + . . .

And I would like to extract each term of this polynomial into a list
like

    { x, x^3/6, (3 x^5)/40, (5 x^7)/112, (35 x^9)/1152, (63 x^11)/
2816, (231 x^13)/13312, (143 x^15)/10240,
         (6435 x^17)/557056,  (12155 x^19)/1245184,  (46189 x^21)/
5505024,  . . . }

Then I would like to take this list and multiply each element in the
list by the integrated polynomial in order to get a list of
polynomials that shows all of the components of the fully multiplied
polynomial in an expanded form. In other words I would like to show
the term by term expansion of the integral multiplied by itself, ie

     Expand[ Integrate[Normal[Series[(1 - t^2)^(-1/2), {t, 0, 50}]],
{t, 0, x}] *
                  Integrate[Normal[Series[(1 - t^2)^(-1/2), {t, 0,
50}]], {t, 0, x}]]

Was working thru an example of what Euler did to compute Zeta[2] and
was looking for patterns in the polynomial coefficients.

Thanks very much ...

-Bob

• Follow-Ups:
  • Re: Extracting terms of a polynomial into a list and then
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Extracting terms of a polynomial into a list and then
    • From: mante <claude.mante@univmed.fr>
  • Re: Extracting terms of a polynomial into a list and then multiply each
    • From: "Thomas Dowling" <thomasgdowling@gmail.com>
  • Re: Extracting terms of a polynomial into a list and then
    • From: Lou Talman <talmanl@mscd.edu>