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

• To: mathgroup at smc.vnet.net
• Subject: [mg90380] Re: [mg90354] Extracting terms of a polynomial into a list and then
• From: DrMajorBob <drmajorbob at att.net>
• Date: Tue, 8 Jul 2008 02:23:59 -0400 (EDT)
• References: <22839460.1215425582193.JavaMail.root@m08>

```Perhaps you mean something like

t=List@@(s=Integrate[Normal[Series[(1-t^2)^(-1/2),{t,0,50}]],{t,0,x}])
{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,(88179 x^23)/12058624,(676039
x^25)/104857600,(1300075 x^27)/226492416,(5014575 x^29)/973078528,(9694845
x^31)/2080374784,(100180065 x^33)/23622320128,(116680311
x^35)/30064771072,(2268783825 x^37)/635655159808,(1472719325
x^39)/446676598784,(34461632205 x^41)/11269994184704,(67282234305
x^43)/23639499997184,(17534158031 x^45)/6597069766656,(514589420475
x^47)/206708186021888,(8061900920775 x^49)/3448068464705536,(5267108601573
x^51)/2392537302040576}

s  t//Short
{x (x+<<24>>+(5267108601573 <<1>>)/2392537302040576),<<25>>}

Bobby

On Mon, 07 Jul 2008 04:05:53 -0500, Bob F <deepyogurt at gmail.com> 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 and
> was looking for patterns in the polynomial coefficients.
>
> Thanks very much ...
>
> -Bob
>
>
>

--
DrMajorBob at longhorns.com

```

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