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Computing Complex Series Solution using Mathematica (using BesselI)


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
\!\(Sinh[z] \[Equal]
    2\ \(\[Sum]\+\(k = 0\)\%\[Infinity] BesselI[2\ k + 1, z]\)\)

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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