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

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=-39/8, b>=a

For fixed z and a=-39/8, b=35/8

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

Input Form

Hypergeometric2F1[-(39/8), 35/8, 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-9491456 - 15720224 z - 38216087 z^2 - 178428250 z^3 + 3368976281 z^4 - 9445843960 z^5 + 11239016880 z^6 - 6269540160 z^7 + 1353580800 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-9491456 - 15720224 z - 38216087 z^2 - 178428250 z^3 + 3368976281 z^4 - 9445843960 z^5 + 11239016880 z^6 - 6269540160 z^7 + 1353580800 z^8) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-9491456 - 15720224 z - 38216087 z^2 - 178428250 z^3 + 3368976281 z^4 - 9445843960 z^5 + 11239016880 z^6 - 6269540160 z^7 + 1353580800 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-4745728 - 4894032 z - 13708851 z^2 - 76237525 z^3 - 1333382397 z^4 + 7500368805 z^5 - 14937089440 z^6 + 14521450320 z^7 - 7014009600 z^8 + 1353580800 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (201595634485245 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]