Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4qa)

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=-29/8

http://functions.wolfram.com/07.23.03.b4qa.01

Input Form

Hypergeometric2F1[-(47/8), -(29/8), 5, z] == (65536 2^(1/4) (-4 Sqrt[1 - z] (19405281792 - 476440095664 z + 6901015970927 z^2 - 101992253418055 z^3 - 2950987246392305 z^4 - 7727457315472175 z^5 - 5088446506136315 z^6 - 791026765451325 z^7 - 4492349309955 z^8 + 98086229475 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (19405281792 - 476440095664 z + 6901015970927 z^2 - 101992253418055 z^3 - 2950987246392305 z^4 - 7727457315472175 z^5 - 5088446506136315 z^6 - 791026765451325 z^7 - 4492349309955 z^8 + 98086229475 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 2 Sqrt[1 - z] (19405281792 - 476440095664 z + 6901015970927 z^2 - 101992253418055 z^3 - 2950987246392305 z^4 - 7727457315472175 z^5 - 5088446506136315 z^6 - 791026765451325 z^7 - 4492349309955 z^8 + 98086229475 z^9) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (38810563584 - 977136793568 z + 14393602462629 z^2 - 212514934795215 z^3 + 7669311277297885 z^4 + 44891861415716085 z^5 + 58269367070949555 z^6 + 21074617445212435 z^7 + 1574578241762175 z^8 - 18185186944665 z^9 + 392344917900 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (440571200644433783925 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

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]