MMa gave me a complicated result involving
Hypergeometric0F1's. It was much less complicated after I discovered this identity:
Hypergeometric0F1[1, -x^2] = BesselJ[0, 2 x]
1) Is there a way to get MMa to validate relationships between functions, for example if I wasn't sure the identity above was true?
FullSimplify[Hypergeometric0F1[1, -x^2] - BesselJ[0, 2 x]]
does return 0, so that worked for the example, but
FullSimplify failing to simplify something to 0 is not a solid proof.
2) Is there a way to tell MMa to convert (for example) all the Hypergeometric functions into whatever Bessel function form it can?