AppellF1

AppellF1[a,b1,b2,c,x,y]

is the Appell hypergeometric function of two variables .

Details

  • 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 twovariable 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.

Examples

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Basic Examples  (3)

Evaluate numerically:

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Evaluate symbolically:

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The defining sum:

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Scope  (4)

Applications  (1)

Properties & Relations  (2)

See Also

Hypergeometric2F1

Tutorials

Introduced in 1999
(4.0)