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Hypergeometric2F1Regularized

Hypergeometric2F1Regularized[a, b, c, z]
is the regularized hypergeometric function _2F_1(a,b;c;z)/Gamma(c).
  • Mathematical function, suitable for both symbolic and numerical manipulation.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Evaluate numerically:
Regularize Hypergeometric2F1 for negative integer values of the parameter c:
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 c:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Series expansion at the origin:
In[1]:=
Click for copyable input
Out[1]=
Scope   (6)
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:
Applications   (1)
Define the fractional derivative of EllipticK:
Check that for integer order Alpha it coincides with the ordinary derivative:
Evaluate derivative of order 1/2:
Properties & Relations   (3)
Evaluate symbolically for numeric third argument:
Use FunctionExpand to expand Hypergeometric2F1Regularized into other functions:
Integrate may give results involving Hypergeometric2F1Regularized:
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