Quote Originally Posted by Exciter View Post
I'm not sure exactly what you wish to know. Something like this would normally be read something like "J prime at zero equals the integral from a to b of the (integral expression)". Often people use the term "partial of F with respect to f" as meaning "partial differential of F with respect to f" since it can't really mean anything else. Sometimes people will say "curly d of" when they are referring to a partial (differential).
"J prime" means first derivative of J. "J double prime" means second derivative of J. After that, people usually say third derivative. But you might hear triple prime. After that it is usually fourth derivative etc.

THis is some kind of integral equation, no? Maybe try here: Mathematical Equations - EqWorld