This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

AppellF1

 AppellF1is 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 has singular lines in two-variable complex space at and , and has branch cut discontinuities along the rays from to in and .
Evaluate numerically:
Evaluate symbolically:
The defining sum:
Evaluate numerically:
 Out[1]=

Evaluate symbolically:
 Out[1]=

The defining sum:
 Out[1]=
 Scope   (4)
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
TraditionalForm formatting:
 Applications   (1)
The Appell system of PDEs for the Picard modular function associated with :
Check that is a solution:
Evaluate integrals in terms of AppellF1:
Use FullSimplify to simplify some expressions involving AppellF1:
New in 4