The Appell's series, AppellF1[a,b1,b2,c,z1,z2], is defined for |z1|<1 and |z2|<1. Why Mathematica gives this result then: AppellF1[1,1,1,2,4,5]?
AppellF1[a,b1,b2,c,z1,z2]
|z1|<1
|z2|<1
AppellF1[1,1,1,2,4,5]