Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7ij)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-43/8, b>=a

For fixed z and a=-43/8, b=-23/8

http://functions.wolfram.com/07.23.03.b7ij.01

Input Form

Hypergeometric2F1[-(43/8), -(23/8), 21/4, z] == (16 2^(1/4) (4 (50310 - 1058445 z + 12397545 z^2 - 129118164 z^3 + 12525096255 z^4 + 42737082608 z^5 + 32207840863 z^6 + 5344266928 z^7 - 2512685 z^8 + 73185 z^9) + (1/Sqrt[1 - z]) (-201240 + 4334400 z - 51681915 z^2 + 540751101 z^3 + 21517598697 z^4 + 25159952081 z^5 - 25574523777 z^6 - 20090813897 z^7 - 1545252485 z^8 + 41007995 z^9 - 1170960 z^10)))/(1149924448365 (1 + Sqrt[1 - z])^(1/4) z^4)

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]