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Hypergeometric2F1Regularized

Hypergeometric2F1Regularized
is the regularized hypergeometric function .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
Evaluate numerically:
Regularize Hypergeometric2F1 for negative integer values of the parameter :
Series expansion at the origin:
Evaluate numerically:
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Click for copyable input
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Regularize Hypergeometric2F1 for negative integer values of the parameter :
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
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Series expansion at the origin:
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:
Automatically evaluate to simpler functions for certain parameters:
Hypergeometric2F1Regularized threads element-wise over lists:
TraditionalForm formatting:
Define the fractional derivative of EllipticK:
Check that for integer order it coincides with the ordinary derivative:
Evaluate derivative of order 1/2:
Evaluate symbolically for numeric third argument:
Use FunctionExpand to expand Hypergeometric2F1Regularized into other functions:
Integrate may give results involving Hypergeometric2F1Regularized:
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