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>