Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b838)

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=-43/8, b>=a

For fixed z and a=-43/8, b=31/8

http://functions.wolfram.com/07.23.03.b838.01

Input Form

Hypergeometric2F1[-(43/8), 31/8, 5, z] == (1/(328163390911125 Pi z^4)) (32768 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-82824192 + 28470816 z + 59287239 z^2 + 275730147 z^3 - 5577818275 z^4 + 17661711185 z^5 - 25737239080 z^6 + 20025623280 z^7 - 8115332160 z^8 + 1353580800 z^9) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (10353024 + 3963267 z - 3801501 z^2 - 3374843175 z^3 + 13063985225 z^4 - 21257737720 z^5 + 17886555440 z^6 - 7709257920 z^7 + 1353580800 z^8) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (10353024 - 1860309 z - 7198587 z^2 + 1967478975 z^3 - 8747733385 z^4 + 17060691530 z^5 - 18339128080 z^6 + 11352363360 z^7 - 3814636800 z^8 + 541432320 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-82824192 + 28470816 z + 59287239 z^2 + 275730147 z^3 - 5577818275 z^4 + 17661711185 z^5 - 25737239080 z^6 + 20025623280 z^7 - 8115332160 z^8 + 1353580800 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

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]