Hmmm, but in the Naruto games [Which I know may or may not be canon] Jiraiya is shown using the rasengan with like different elements on it like fire and water, also he's able to use two Rasengan at once.you mean that big ball rasengan that he used againce pain?if not then he didnt do anything to it.he teached naruto make odama adn after that naruto made the rasenshuriken whit the help of kakashi and yamato.
So to say Jiraiya NEVER expanded upon the Rasengan at all is a little questionable.
But yea, Naruto was the first one to expand upon the Rasengan like Minato had intended, by adding the wind element into it, which Jiraiya wasn't able to do because he's a fire type I think.