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

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=7/8

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

Input Form

Hypergeometric2F1[-(29/8), 7/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-86474752 + 762396544 z - 2997574125 z^2 + 6954028900 z^3 - 10872073030 z^4 - 1458521460 z^5 + 632805195 z^6 - 163475400 z^7 + 18849600 z^8) EllipticE[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-86474752 + 762396544 z - 2997574125 z^2 + 6954028900 z^3 - 10872073030 z^4 - 1458521460 z^5 + 632805195 z^6 - 163475400 z^7 + 18849600 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 + 762396544 z - 2997574125 z^2 + 6954028900 z^3 - 10872073030 z^4 - 1458521460 z^5 + 632805195 z^6 - 163475400 z^7 + 18849600 z^8) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-86474752 + 794824576 z - 3274605789 z^2 + 8004654385 z^3 - 13210913170 z^4 + 12532005090 z^5 - 6981389745 z^6 + 2836531005 z^7 - 690030000 z^8 + 75398400 z^9) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (2749421275575975 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]