Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b87o)

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=39/8

http://functions.wolfram.com/07.23.03.b87o.01

Input Form

Hypergeometric2F1[-(43/8), 39/8, 5, z] == (1/(10173065118244875 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-8 (41412096 + 115177392 z + 450599193 z^2 + 3165194439 z^3 - 91518448025 z^4 + 363999345945 z^5 - 636711724960 z^6 + 577534473360 z^7 - 267196849920 z^8 + 50082489600 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-10353024 - 36316467 z - 139765824 z^2 - 104381533575 z^3 + 517655583050 z^4 - 1025547743280 z^5 + 1016620190560 z^6 - 504344206080 z^7 + 100164979200 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-10353024 - 30492891 z - 118170063 z^2 + 61278982875 z^3 - 336614890765 z^4 + 780322257420 z^5 - 970616070320 z^6 + 681564848640 z^7 - 255826771200 z^8 + 40065991680 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 4 (41412096 + 115177392 z + 450599193 z^2 + 3165194439 z^3 - 91518448025 z^4 + 363999345945 z^5 - 636711724960 z^6 + 577534473360 z^7 - 267196849920 z^8 + 50082489600 z^9) 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]