Re: problems with sum functions/ factoring the factorial
- To: mathgroup at smc.vnet.net
- Subject: [mg65821] Re: problems with sum functions/ factoring the factorial
- From: Roger Bagula <rlbagulatftn at yahoo.com>
- Date: Mon, 17 Apr 2006 02:29:17 -0400 (EDT)
- References: <e1sns1$86r$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
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 >