is the hypergeometric function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The function has the series expansion , where is the Pochhammer symbol.
- 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.
- Hypergeometric2F1 can be used with Interval and CenteredInterval objects. »
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Basic Examples (7)
Numerical Evaluation (5)
Evaluate Hypergeometric2F1 efficiently at high precision:
Hypergeometric2F1 threads elementwise over lists:
Specific Values (6)
Hypergeometric2F1 automatically evaluates to simpler functions for certain parameters:
Exact value of Hypergeometric2F1 at unity:
Function Properties (9)
Real domain of Hypergeometric2F1:
Complex domain of Hypergeometric2F1:
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:
Two players roll dice. If the total of both numbers is less than 10, the second player is paid 4 cents; otherwise, the first player is paid 9 cents. Is the game fair? Compute the probability that the first player gets paid:
Properties & Relations (2)
Possible Issues (1)
However, if is a negative integer, Hypergeometric2F1 returns a polynomial:
Wolfram Research (1988), Hypergeometric2F1, Wolfram Language function, https://reference.wolfram.com/language/ref/Hypergeometric2F1.html (updated 2022).
Wolfram Language. 1988. "Hypergeometric2F1." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/Hypergeometric2F1.html.
Wolfram Language. (1988). Hypergeometric2F1. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Hypergeometric2F1.html