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

*To*: mathgroup at smc.vnet.net*Subject*: [mg90384] Re: Extracting terms of a polynomial into a list and then multiply*From*: Bob F <deepyogurt at gmail.com>*Date*: Tue, 8 Jul 2008 02:24:45 -0400 (EDT)*References*: <g4sm99$p$1@smc.vnet.net>

On Jul 7, 3:05 am, Bob F <deepyog... 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^2= 1)/ > 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 Found it -- one way is to use the "Apply[List,polynomial]]". So in this example: Apply[List, Integrate[Normal[Series[(1 - t^2)^(-1/2), {t, 0, 50}]], {t, 0, x}]] would give the desired list, then what I was really after would be Expand[Apply[List, Integrate[ Normal[Series[(1 - t^2)^(-1/2), {t, 0, 20}]], {t, 0, x}]]* Integrate[Normal[Series[(1 - t^2)^(-1/2), {t, 0, 20}]], {t, 0, x}]] Anyone have a different way? Thanks... -Bob