Re: MathKernel crashes

*To*: mathgroup at smc.vnet.net*Subject*: [mg72850] Re: MathKernel crashes*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 22 Jan 2007 04:15:15 -0500 (EST)*References*: <eosgop$9ai$1@smc.vnet.net>

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