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is there any definite method or algorithm,software to get exact function or expression from series.e.g we get series solution of differential equation and we want exact expression rather than approximation series ?

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Usually I do this the other way around. I have a power series, and want its sum, so if I can find a DE it satisfies, then solve the DE to get the result! –  Gerald Edgar Sep 11 '11 at 12:50
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up vote 2 down vote accepted

In some cases yes, see:

http://www.reduce-algebra.com/docs/qsum.pdf

and references therein...

EDIT A canonical reference is Petkovsek-Zeiberger's A=B.

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thanks very much, i would like to see more such stuff –  anksh Sep 11 '11 at 6:41
    
More stuff in Wilf's book generatingfunctionology –  Gerald Edgar Sep 11 '11 at 12:49
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