Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9vr)

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=-13/8

http://functions.wolfram.com/07.23.03.b9vr.01

Input Form

Hypergeometric2F1[-(39/8), -(13/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (303726592 - 4801490304 z + 38741778335 z^2 - 230257439230 z^3 + 1441575360225 z^4 + 12427887848320 z^5 + 7745802131025 z^6 + 187433968410 z^7 - 13828550385 z^8 + 665367300 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (303726592 - 4801490304 z + 38741778335 z^2 - 230257439230 z^3 + 1441575360225 z^4 + 12427887848320 z^5 + 7745802131025 z^6 + 187433968410 z^7 - 13828550385 z^8 + 665367300 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (303726592 - 4801490304 z + 38741778335 z^2 - 230257439230 z^3 + 1441575360225 z^4 + 12427887848320 z^5 + 7745802131025 z^6 + 187433968410 z^7 - 13828550385 z^8 + 665367300 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (303726592 - 4991319424 z + 41711565935 z^2 - 253993309050 z^3 + 1581735616825 z^4 - 27023411859500 z^5 - 49278701760295 z^6 - 11799601519290 z^7 + 389916327255 z^8 - 28389004800 z^9 + 1330734600 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (10111470178724709795 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]