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

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=-19/8, b>=a

For fixed z and a=-19/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(19/8), -(7/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-6848512 + 74504320 z - 387627075 z^2 + 1350868365 z^3 - 4251944070 z^4 + 28450376322 z^5 + 15362847145 z^6 + 15247505 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (11132673648801705 Pi (1 + Sqrt[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]