Re: Kei Ker from Bessel functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg4197] Re: [mg4137] Kei Ker from Bessel functions*From*: jpk at apex.mpe.FTA-Berlin.de (Jens-Peer Kuska)*Date*: Thu, 13 Jun 1996 23:10:08 -0400*Sender*: owner-wri-mathgroup at wolfram.com

> Hello everybody, > does someone has available Kei, Ker, Bei, Ber functions (from > Bessel functions) in working examples? Something goes wrong when > I make Ker and Kei functions from Im[D[BesselJ[n,x],x]. > Please write directly to 100332.166 at Compuserve.Com > Thanks in advance, > Peter I don't know Your definiton of Kelvin functions but the definitions from Abramowitz/Stegun (eqn 9.9.1 & 9.9.2) can used directly with out problems i.e. In[]:= KelvinKer[nu_?NumberQ,x_?NumberQ]:= Re[Exp[-nu*Pi*I/2]*BesselK[nu,x*Exp[Pi I/4]]] KelvinKei[nu_?NumberQ,x_?NumberQ]:= Im[Exp[-nu*Pi*I/2]*BesselK[nu,x*Exp[Pi I/4]]] In[]:= KelvinKer[2,0.5] Out[]= 0.476909 Derivation of Bessel functions via D[BesselJ[n,x],x] will only give You the usual formula D[BesselJ[nu,x],x]:=BesselJ[nu-1,x]- nu*BesselJ[nu,x]/x Hope that helps Jens ==== [MESSAGE SEPARATOR] ====