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 ?



method for getting function from power series/perturbation series
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.


