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AppellF1

AppellF1
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 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 .
Evaluate numerically:
Evaluate symbolically:
The defining sum:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
Evaluate symbolically:
In[1]:=
Click for copyable input
Out[1]=
 
The defining sum:
In[1]:=
Click for copyable input
Out[1]=
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:
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:
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