Re: problems with sum functions/ factoring the factorial
- To: mathgroup at smc.vnet.net
- Subject: [mg65852] Re: problems with sum functions/ factoring the factorial
- From: Roger Bagula <rlbagulatftn at yahoo.com>
- Date: Tue, 18 Apr 2006 06:56:49 -0400 (EDT)
- References: <e1sns1$86r$1@smc.vnet.net> <e1vhef$a94$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
This cf[n] is in the OEIS already - see A049614 Roger Bagula wrote: > Another inferior definition of the primorial function exists at: > http://mathworld.wolfram.com/Primorial.html > There are in fact 396 sequences in OEIS that mention the name: > http://www.research.att.com/~njas/sequences/?q=primorial&language=english&go=Search > The one I'm refering to is: > http://www.research.att.com/~njas/sequences/?q=A034386&sort=0&fmt=0&language=english&go=Search > Also see: > http://www.research.att.com/~njas/sequences/?q=A117683&sort=0&fmt=0&language=english&go=Search > Roger > Roger Bagula wrote: > > >>I have no problem constructing the Primorial or Compositorial functions >>that factor the factorial as: >>cf[n]*p[n]=n! >>But trying to get the sine and cosine constructed functions to plot >>seems to be a problem here: >>Clear[f, g, cf, p, CeS, CeC, PeS, PeC] >>f[n_] := If[PrimeQ[n] == True, 1, n] >>cf[0] = 1; >>cf[n_Integer?Positive] := cf[n] = f[n]*cf[n - 1] >>g[n_] := If[PrimeQ[n] == True, n, 1] >>p[0] = 1; >>p[n_Integer?Positive] := p[n] = g[n]*p[n - 1] >>Ce = 1 + Sum[1/cf[n], {n, 1, 1000}]; >>N[%, 100] >>Pe = 1 + Sum[1/p[n], {n, 1, 1000}]; >>N[%, 100] >>CeS[x_] := 1 + NSum[(-1)^n*p[2*n + 1]*x^(2*n + 1)/(2*n + 1)!, {n, 1, 100}]; >>CeC[x_] := 1 + NSum[(-1)^n*p[2*n]*x^(2*n)/(2*n)!, {n, 1, 100}]; >>ParametricPlot[{CeC[x], CeS[x]}, {x, 0, 2*Pi}] >>PeS[x_] := 1 + NSum[(-1)^n*cf[2*n + 1]*x^(2*n + 1)/(2*n + 1)!, {n, 1, 100}]; >>PeC[x_] := 1 + NSum[(-1)^n*cf[2*n]*x^(2*n)/(2*n)!, {n, 1, 100}]; >>ParametricPlot[{PeC[x], PeS[x]}, {x, 0, 2*Pi}] >> >>Alernative functions: >>CeS1[x_] := 1 + NSum[(-1)^n*x^(2*n + 1)/cf[2*n + 1], {n, 1, 100}]; >>CeC1[x_] := 1 + NSum[(-1)^n*x^(2*n)/cf[2*n], {n, 1, 100}]; >>ParametricPlot[{CeC[x], CeS[x]}, {x, 0, 2*Pi}] >>PeS1[x_] := 1 + NSum[(-1)^n*x^(2*n + 1)/p[2*n + 1], {n, 1, 100}]; >>PeC1[x_] := 1 + NSum[(-1)^n*x^(2*n)/p[2*n], {n, 1, 100}]; >>ParametricPlot[{PeC1[x], PeS1[x]}, {x, 0, 2*Pi}] >> >>In addition this function seem to come up with the wrong sign: >>Pe[x_] := 1 + NSum[cf[n]*x^n/n!, {n, 1, 100}]; >>Plot[Pe[x], {x, 0, 5}] >> >>Or alternatively: >>Pe1[x_] := 1 + NSum[x^n/p[n], {n, 1, 100}]; >>Plot[Pe1[x], {x, 0, 5}] >> >>Ce*Pe~ 5*E (low) >>Roger >> > >