How simplify sum ?

• Subject: How simplify sum ?
• From: Aleksas Domarkas
• Date: Tue, 5 Jun 2012 00:05:37 +0300

How simplify sum
sum(x^(3*n)/(3*n)!,n,0,inf) ?

The answer should be
(2*%e^(-x/2)*cos((sqrt(3)*x)/2))/3+%e^x/3

This is solution of the problem
y'' + y' + y = exp(x), y(0)=1, y'(0)=0.

Aleksas D

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