Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7r1)

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=7/8

http://functions.wolfram.com/07.23.03.b7r1.01

Input Form

Hypergeometric2F1[-(43/8), 7/8, 4, z] == (1/(9702221992155 Pi z^3)) (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-120785280 + 1069138455 z - 4410549990 z^2 - 3379705502 z^3 + 3602190248 z^4 - 2595689217 z^5 + 1197872598 z^6 - 320457072 z^7 + 37870560 z^8) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 6 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (7549080 - 61336275 z - 1347510780 z^2 + 1516632662 z^3 - 1149738356 z^4 + 555001941 z^5 - 154547952 z^6 + 18935280 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (15098160 - 131165265 z + 2425519404 z^2 - 2761031030 z^3 + 2479207172 z^4 - 1526550513 z^5 + 611885352 z^6 - 144088464 z^7 + 15148224 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-120785280 + 1069138455 z - 4410549990 z^2 - 3379705502 z^3 + 3602190248 z^4 - 2595689217 z^5 + 1197872598 z^6 - 320457072 z^7 + 37870560 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

Standard Form

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MathML Form

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</annotation-xml> </semantics> </math>

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]