Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.afe1)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-7/4, b>=a

For fixed z and a=-7/4, b=5

http://functions.wolfram.com/07.23.03.afe1.01

Input Form

Hypergeometric2F1[-(7/4), 5, -(21/4), z] == (1/(1018368 (-1 + z)^9)) (4 (-1 + z) (254592 - 1612416 z + 3958656 z^2 - 4213632 z^3 + 716800 z^4 + 1232896 z^5 + 6909952 z^6 - 12673093 z^7 + 9433325 z^8 - 3430735 z^9 + 504735 z^10) - 231 Sqrt[1 - z] z^(25/4) (43993 - 66748 z + 45510 z^2 - 15580 z^3 + 2185 z^4) Beta[z, 3/4, 1/2])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]