AppellF1[a, b1, b2, c, x, y]
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 Re(x)=1 and Re(y)=1, and has branch cut discontinuities along the rays from to in and .
  • FullSimplify and FunctionExpand include transformation rules for AppellF1.
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