Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4nr)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-37/8

http://functions.wolfram.com/07.23.03.b4nr.01

Input Form

Hypergeometric2F1[-(47/8), -(37/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (22964371456 - 588372313984 z + 8211334728051 z^2 - 91788631955384 z^3 + 1205617158650996 z^4 + 34255113459906360 z^5 + 98852758305979090 z^6 + 82430547341842040 z^7 + 21466025744703540 z^8 + 1359073553477640 z^9 + 1927225294995 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (22964371456 - 588372313984 z + 8211334728051 z^2 - 91788631955384 z^3 + 1205617158650996 z^4 + 34255113459906360 z^5 + 98852758305979090 z^6 + 82430547341842040 z^7 + 21466025744703540 z^8 + 1359073553477640 z^9 + 1927225294995 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (22964371456 - 588372313984 z + 8211334728051 z^2 - 91788631955384 z^3 + 1205617158650996 z^4 + 34255113459906360 z^5 + 98852758305979090 z^6 + 82430547341842040 z^7 + 21466025744703540 z^8 + 1359073553477640 z^9 + 1927225294995 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (22964371456 - 602725046144 z + 8576712679171 z^2 - 96861488801714 z^3 + 1262170679740516 z^4 - 44135197134620480 z^5 - 270666960717911870 z^6 - 409055738837001860 z^7 - 202914997706624060 z^8 - 31367134410371760 z^9 - 984812125742445 z^10 + 3854450589990 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (20354389469772840817335 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]