Proof and generalization of conjectures of Ramanujan Machine

The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference equation. In this paper, we prove 38 conjectures by solving the equation in two ways, use of a differential equation or application of Petkovsek's algorithm. Especially, in the former way, we can get strong generalization of 31 conjectures.