The F4U Corsair was designed around a P&W R2800 matched to a 13' 4" prop. The cut and paste from wiki explains what pretty much every doco I've read or seen says about why they have the inverted gull wing. Consider also that it was designed from the start to be a carrier based fighter and needed solid landing gear.
To accommodate a folding wing the designers considered retracting the main landing gear rearward but, for the chord of wing that was chosen, it was difficult to make the landing gear struts long enough to provide ground clearance for the large propeller. Their solution was an inverted gull wing, which considerably shortened the required length of the struts.[24] The anhedral of the wing's center-section also permitted the wing and fuselage to meet at the optimum angle for minimizing drag, without using wing root fairings.[24] The bent wing, however, was heavier and more difficult to construct, offsetting these benefits.