Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7lp)

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=-9/8

http://functions.wolfram.com/07.23.03.b7lp.01

Input Form

Hypergeometric2F1[-(43/8), -(9/8), 4, z] == (1/(48511109960775 Pi z^3)) (1024 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-6588288 + 113493555 z - 1306179567 z^2 - 68642186554 z^3 - 83696599686 z^4 - 667426545 z^5 + 116717325 z^6 - 16395480 z^7 + 1193400 z^8) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (205884 - 3397086 z - 3909479805 z^2 - 5584186978 z^3 - 158944050 z^4 + 28014810 z^5 - 4009365 z^6 + 298350 z^7) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (823536 - 14051583 z + 9635834439 z^2 + 17747734526 z^3 + 3718736910 z^4 - 315215955 z^5 + 53514555 z^6 - 7059420 z^7 + 477360 z^8) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-6588288 + 113493555 z - 1306179567 z^2 - 68642186554 z^3 - 83696599686 z^4 - 667426545 z^5 + 116717325 z^6 - 16395480 z^7 + 1193400 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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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]