TITLE: Software, techniques and tricks of experimental mathematics to conjecture possible closed forms
QUESTION [6 upvotes]: It often happens that people conjecture possible closed forms of integrals, series, and so on starting from a numerical value calculated to very high precision. 
What are the techniques, tricks, methods, and softwares (in particular, what are the function of Mathematica and Maple) that help in formulating such conjectures?
Any reference is highly appreciated.

REPLY [2 votes]: One of the oldest ISC (Inverse Symbolic Computer) is the Plouffe's inverter, cited here for memory because it is no longer available at http://pi.lacim.uqam.ca/
Others were already quoted in the peceeding answers : http://oldweb.cecm.sfu.ca/
http://oldweb.cecm.sfu.ca/projects/ISC/ISCmain.html
Also, WolframAlpha provides such tool :  https://mathematica.stackexchange.com/questions/55818/lookup-in-inverse-symbolic-calculator-from-mathematica
I am rising here to mention that, surprisingly, it is not very difficult to built an "homemade" ISC on a personal computer. Of course, it will be much less effective than the professionnal ISC cited above. Doing such a software by ourself is more an educational game to experiment some elementary features of those kind of tools. There is a short general-public paper publish on Scribd which gives an hint on the subjet (in French, not translated yet) : http://fr.scribd.com/doc/14161596/Mathematiques-experimentales