Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b68r)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-33/8

http://functions.wolfram.com/07.23.03.b68r.01

Input Form

Hypergeometric2F1[-(45/8), -(33/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (527400960 - 12742089600 z + 165635710525 z^2 - 1693935872200 z^3 + 19797167071500 z^4 + 1476934484650184 z^5 + 4911083987403790 z^6 + 4480540511940360 z^7 + 1255731664739020 z^8 + 84544489143800 z^9 + 5582917725 z^10) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (527400960 - 12742089600 z + 165635710525 z^2 - 1693935872200 z^3 + 19797167071500 z^4 + 1476934484650184 z^5 + 4911083987403790 z^6 + 4480540511940360 z^7 + 1255731664739020 z^8 + 84544489143800 z^9 + 5582917725 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (527400960 - 12742089600 z + 165635710525 z^2 - 1693935872200 z^3 + 19797167071500 z^4 + 1476934484650184 z^5 + 4911083987403790 z^6 + 4480540511940360 z^7 + 1255731664739020 z^8 + 84544489143800 z^9 + 5582917725 z^10) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (527400960 - 12939864960 z + 170359914925 z^2 - 1754771431300 z^3 + 20416084201500 z^4 + 387260164224584 z^5 + 524554173949246 z^6 - 349089585460560 z^7 - 481949539417220 z^8 - 96942587597800 z^9 - 2674217590275 z^10 + 22331670900 z^11) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (283748727564102575775 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)

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]