Re: MathKernel crashes

*To*: mathgroup at smc.vnet.net*Subject*: [mg72861] Re: MathKernel crashes*From*: "nandan" <joshi.nandan at gmail.com>*Date*: Tue, 23 Jan 2007 04:35:07 -0500 (EST)*References*: <eosgop$9ai$1@smc.vnet.net><ep1t7a$ga7$1@smc.vnet.net>

Hi: I'm aware that these are recursive functions for this Legendre Polynomial, but they were taking lot of time, so I went for recursion. But in fact, it is take more time and my kernel quits. But I think, you have replied to this problem in this post: http://groups-beta.google.com/group/comp.soft-sys.math.mathematica/browse_frm/thread/922e6b5d1a472346 Thanx again! Regards, nandan On Jan 22, 9:39 am, Peter Pein <pet... at dordos.net> wrote: > nandan schrieb: > > > > > Hallo: > > > MathKernel crashes, since I use recursive function for calculation. I > > have 2 of the important functions for my calculation as given below: > > $RecursionLimit=Infinity; > > > pi[0, \[Theta]_] := 0; > > pi[1, \[Theta]_] := 1; > > pi[i_, \[Theta]_]\ := pi[i, \[Theta]] = ((2 i - 1)/(i - 1)) > > Cos[\[Theta]] pi[i - 1, \[Theta]] - (i/(i - 1)) pi[i - 2,\[Theta]]); > > \[Tau][i_, \[Theta]_] := \[Tau][i, \[Theta]] = i Cos[\[Theta]] pi[i, > > \[Theta]] - (i + 1)pi[i - 1, \[Theta]]; > > > In this case, I can get solution to any numerical value like pi[14, > > \[Pi]/3]. But quite a few times, it happened that MathKernel quitted, I > > started again, but it started another processor parallel to that. Later > > I wanted to calculate another function as follows: > > S1Temp[i_, \[Theta]_] := ((2 l + 1)/(l (l + 1))) (an[l] pi[l, \[Theta]] > > + bn[l] \[Tau][l, \[Theta]]); > > > But in this case, whenever I try to calculate S1Temp[14, \[Pi]/3], it > > simply quits and, sometimes crashes. I have to always restart > > Mathematica to start over again. > > > I do not know what is exactly going wrong. If any better solution is > > possible for this recursive solution, will also be appreciated. > > > Regards, > > nandan > Hi Nandan, > > why don't you simply use RSolve? > > Needs["DiscreteMath`RSolve`"]; > > pi[i_, t_] = FullSimplify[p[i] /. > First[RSolve[ > {p[i] == ((2*i - 1)*Cos[t]*p[i - 1] - i*p[i - 2])/(i - 1), > p[0] == 0, p[1] == 1}, p, i] > ]] /. ((x_)^2)^(-2^(-1)) :> 1/Abs[x] > > --> -(LegendreP[i, 1, 2, Cos[t]]/Abs[Sin[t]]) > > pi[14, Pi/3] > --> 30439185/8388608