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Re: Re: Computing Complex Series Solution using Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg54689] Re: [mg54644] Re: Computing Complex Series Solution using Mathematica
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Sun, 27 Feb 2005 01:29:13 -0500 (EST)
• References: <cvhiv9$s5r$1@smc.vnet.net> <200502250618.BAA02383@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Jens-Peer Kuska wrote:

>Hi,
>
>can you tell us *what* you plan to do ?
>Sinh[lambda*x]
>is no complex series,
>
I apologize  for the misunderstanding, the series is not a power series 
but, it is a series obtained when solving a PDE using the seperation of 
variables method, the lamda's are the ordered pair of eigenvalues with 
Im[lamda[[1]]]<Im[lamda[[2]]....etc

> if you whish to use the series expansion
>Sinh[y]:> Sum[y^(2n + 1)/(2n + 1)!, {n, 0, Infinity}]
>  
>
I want to do something similar, but I want to expand it using BesselI 
function if possible, much in the vein given here
http://functions.wolfram.com/ElementaryFunctions/Sinh/06/06/0001/

>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 
>  
>
I was not aware of the new symbol, thank you i will try and investigate 
further.

Above all

Thank you for your response Jens

Regards,
Pratik Desai

>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
>>
>>    
>>
>
>
>  
>

• References:
  • Re: Computing Complex Series Solution using Mathematica
    • From: "Jens-Peer Kuska" <kuska@informatik.uni-leipzig.de>