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MathGroup Archive 2005

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Re: Computing Complex Series Solution using Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54644] Re: Computing Complex Series Solution using Mathematica
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 25 Feb 2005 01:18:42 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <cvhiv9$s5r$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

can you tell us *what* you plan to do ?
Sinh[lambda*x]
is no complex series, if you whish to use the series expansion
Sinh[y]:> Sum[y^(2n + 1)/(2n + 1)!, {n, 0, Infinity}]

you should do that, if you use Sum[] Mathematica will simplify it to 
Sinh[x], if you whant to keep the series form, you should use the new symbol 
"sum" instead of Sum in the expression above. Anyway it seems to be better 
to work with a sum Sinh[] and not with the power series.

Regards

  Jens



"Pratik Desai" <pdesai1 at umbc.edu> schrieb im Newsbeitrag 
news:cvhiv9$s5r$1 at smc.vnet.net...

> Hello All,
>
> I am trying to check the convergence or lack there of a complex series
>
> Sinh[lamda*x]
>
> where the first six lamda are given as
> lamda={-0.331+3.162*I,-0.435+6.234*I,-0.093+9.418*I,-0.203+12.566*I,-0.365+15.669*I};
> x=Range[0,1,0.1];
>
> I want to do more efficiently the following:
>
> s4=Sinh[lamda[[1]]*x]+Sinh[lamda[[2]]*x]+Sinh[lamda[[3]]*x]+Sinh[lamda[[4]]*x]
>
> I tried using Sum but to no great success, however I found a neat
> mathematica notebook on the function Sinh and I found the following
> expansion of sinh
>
> I was wondering how I could implement the above series in my application
> or anyother approach that would be more feasible .
>
> Thanks
>
> Pratik Desai
> 



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