Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4t1)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-21/8

http://functions.wolfram.com/07.23.03.b4t1.01

Input Form

Hypergeometric2F1[-(47/8), -(21/8), 6, z] == (524288 2^(1/4) (2 Sqrt[1 - z] (14275149824 - 288123824768 z + 3070831388209 z^2 - 25201008739335 z^3 + 231020574584345 z^4 + 3742913573805125 z^5 + 5500634280168895 z^6 + 1632656319723675 z^7 + 21506589611715 z^8 - 1127653410585 z^9 + 40587405300 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (14275149824 - 288123824768 z + 3070831388209 z^2 - 25201008739335 z^3 + 231020574584345 z^4 + 3742913573805125 z^5 + 5500634280168895 z^6 + 1632656319723675 z^7 + 21506589611715 z^8 - 1127653410585 z^9 + 40587405300 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (14275149824 - 288123824768 z + 3070831388209 z^2 - 25201008739335 z^3 + 231020574584345 z^4 + 3742913573805125 z^5 + 5500634280168895 z^6 + 1632656319723675 z^7 + 21506589611715 z^8 - 1127653410585 z^9 + 40587405300 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (14275149824 - 297045793408 z + 3249445018209 z^2 - 27091420547815 z^3 + 246469756154765 z^4 - 6146775035526315 z^5 - 21459074469295045 z^6 - 15046921605914365 z^7 - 2032559758599825 z^8 + 44243654060775 z^9 - 2299952967000 z^10 + 81174810600 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (2555312963737715946765 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]