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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

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