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

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=43/8

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

Input Form

Hypergeometric2F1[-(39/8), 43/8, 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (-1186432 - 11743823 z - 135281055 z^2 + 5431807150 z^3 - 24402473200 z^4 + 42228644640 z^5 - 32215223040 z^6 + 9105907200 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1186432 - 11743823 z - 135281055 z^2 + 5431807150 z^3 - 24402473200 z^4 + 42228644640 z^5 - 32215223040 z^6 + 9105907200 z^7) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-1186432 - 11743823 z - 135281055 z^2 + 5431807150 z^3 - 24402473200 z^4 + 42228644640 z^5 - 32215223040 z^6 + 9105907200 z^7) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-1186432 - 11002303 z - 127819510 z^2 - 3305013215 z^3 + 30425812900 z^4 - 88410554960 z^5 + 117663087360 z^6 - 74446944000 z^7 + 18211814400 z^8) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (9034375425075 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)

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]