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AppellF1

AppellF1[a, b1, b2, c, x, y]
is the Appell hypergeometric function of two variables F_1(a;b_1,b_2;c;x,y).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • F_1(a;b_1,b_2;c;x,y) has series expansion ∑_(m=0)^(∞)∑_(n=0)^(∞)(a)_(m+n)(b_1)_m(b_2)_n/(m!n!(c)_(m+n))x^my^n.
  • F_1(a;b_1,b_2;c;x,y) reduces to _2F_1(a,b;c;z) when x=0 or y=0.
  • 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 (x,y) space at Re(x)=1 and Re(y)=1, and has branch cut discontinuities along the rays from 1 to ∞ in x and y.
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