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

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=-29/8, b>=a

For fixed z and a=-29/8, b=-1/8

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

Input Form

Hypergeometric2F1[-(29/8), -(1/8), 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (86474752 - 948857728 z + 4937935821 z^2 - 16926242515 z^3 + 50462298250 z^4 + 465184535490 z^5 + 2216951385 z^6 - 337999695 z^7 + 27601200 z^8) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (86474752 - 948857728 z + 4937935821 z^2 - 16926242515 z^3 + 50462298250 z^4 + 465184535490 z^5 + 2216951385 z^6 - 337999695 z^7 + 27601200 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (86474752 - 948857728 z + 4937935821 z^2 - 16926242515 z^3 + 50462298250 z^4 + 465184535490 z^5 + 2216951385 z^6 - 337999695 z^7 + 27601200 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (86474752 - 981285760 z + 5284890429 z^2 - 18685384081 z^3 + 56351912890 z^4 + 17742771630 z^5 - 68008781775 z^6 + 9503898195 z^7 - 1404901080 z^8 + 110404800 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (112726272298614975 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]