Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8uz)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-11/8

http://functions.wolfram.com/07.23.03.b8uz.01

Input Form

Hypergeometric2F1[-(41/8), -(11/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-73891840 + 1188908160 z - 9692465805 z^2 + 57309981630 z^3 - 344610987435 z^4 - 11355196020876 z^5 - 10967373538731 z^6 - 797251922082 z^7 + 70640704827 z^8 - 6573738864 z^9 + 348767496 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (2309120 - 35475660 z + 277277055 z^2 - 1591899210 z^3 - 663700870305 z^4 - 734173626762 z^5 - 65517899139 z^6 + 5798825802 z^7 - 542967579 z^8 + 29063958 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-9236480 + 147098160 z - 1187886645 z^2 + 6975973290 z^3 - 1657983728115 z^4 - 2440173819672 z^5 - 588700961451 z^6 + 11709755442 z^7 - 1092163149 z^8 + 58127916 z^9) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-73891840 + 1188908160 z - 9692465805 z^2 + 57309981630 z^3 - 344610987435 z^4 - 11355196020876 z^5 - 10967373538731 z^6 - 797251922082 z^7 + 70640704827 z^8 - 6573738864 z^9 + 348767496 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (2118118458465234225 Pi 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]