is the Appell hypergeometric function of two variables .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- has series expansion .
- reduces to when or .
- For certain special arguments, AppellF1 automatically evaluates to exact values.
- AppellF1 can be evaluated to arbitrary numerical precision.
- AppellF1[a,b1,b2,c,x,y] has singular lines in two‐variable complex space at and , and has branch cut discontinuities along the rays from to in and .
- FullSimplify and FunctionExpand include transformation rules for AppellF1.
Introduced in 1999