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Re: Extracting terms of a polynomial into a list and then multiply

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90370] Re: Extracting terms of a polynomial into a list and then multiply
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Tue, 8 Jul 2008 02:22:04 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <g4sm99$p$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de

Hi,

ser = Integrate[
   Normal[Series[(1 - t^2)^(-1/2), {t, 0, 50}]], {t, 0, x}];
MapIndexed[x^#2[[1]]*# &, CoefficientList[ser, x]]

??

Regards
   Jens

Bob F wrote:
> 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
> 
> 


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