Re: Substitute values in functions!!!
- To: mathgroup at smc.vnet.net
- Subject: [mg52255] Re: Substitute values in functions!!!
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 18 Nov 2004 01:44:55 -0500 (EST)
- Organization: The University of Western Australia
- References: <cneu7f$q8j$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <cneu7f$q8j$1 at smc.vnet.net>, davidx at x-mail.net (david Lebonvieux) wrote: > How can substitute some values(the zeros of BesselJ function) in this > Integrals? > j0[n_] := x /. FindRoot[BesselJ[0, x] == 0, {x, n 2.5}] Change this to j0[n_] := FindRoot[BesselJ[0, x] == 0, {x, n*2.5}] so that the result is a replacement rule instead of a value. > \!\(s\_l = Array[j0, \ 10]\) > > Integrate[BesselJ[0,s0*r/R] BesselJ[0,s2*r/R] BesselJ[0,s3*r/R],{r,0,R}] By a change of variables r -> R r, this integral becomes R Integrate[BesselJ[0,s0 r] BesselJ[0,s2 r] BesselJ[0,s3 r],{r,0,1}] > where s0, s1,s2,the Zero-Poles of BesselJ. Substitute the first three zeros into the integrand: Times @@ (BesselJ[0, x r] /. Array[j0, 3]) Compute the integral numerically: R NIntegrate[%, {r, 0, 1}] Cheers, Paul -- Paul Abbott Phone: +61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul