is the hypergeometric function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The function has the series expansion .
- For certain special arguments, Hypergeometric2F1 automatically evaluates to exact values.
- Hypergeometric2F1 can be evaluated to arbitrary numerical precision.
- Hypergeometric2F1 automatically threads over lists.
- Hypergeometric2F1[a,b,c,z] has a branch cut discontinuity in the complex plane running from to .
- FullSimplify and FunctionExpand include transformation rules for Hypergeometric2F1.
Examplesopen allclose all
Basic Examples (7)
Numerical Evaluation (4)
Specific Values (6)
Hypergeometric2F1 automatically evaluates to simpler functions for certain parameters:
Exact value of Hypergeometric2F1 at unity:
Series Expansions (6)
Taylor expansion for Hypergeometric2F1:
General term in the series expansion of Hypergeometric2F1:
Expand Hypergeometric2F1 in a series near :
Expand Hypergeometric2F1 in a series around :
Apply Hypergeometric2F1 to a power series:
Properties & Relations (2)
Possible Issues (1)
However, if is a negative integer, Hypergeometric2F1 returns a polynomial: