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>*Reply-to*: drmajorbob at longhorns.com

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[2] and > was looking for patterns in the polynomial coefficients. > > Thanks very much ... > > -Bob > > > -- DrMajorBob at longhorns.com