Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5l1)

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=35/8

http://functions.wolfram.com/07.23.03.b5l1.01

Input Form

Hypergeometric2F1[-(47/8), 35/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-14275149824 + 16449879680 z + 22289674095 z^2 + 43753804705 z^3 + 169354038035 z^4 - 2864179716693 z^5 + 8283504041890 z^6 - 11228752776400 z^7 + 8213605202400 z^8 - 3152489683200 z^9 + 500824896000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-14275149824 + 16449879680 z + 22289674095 z^2 + 43753804705 z^3 + 169354038035 z^4 - 2864179716693 z^5 + 8283504041890 z^6 - 11228752776400 z^7 + 8213605202400 z^8 - 3152489683200 z^9 + 500824896000 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-14275149824 + 16449879680 z + 22289674095 z^2 + 43753804705 z^3 + 169354038035 z^4 - 2864179716693 z^5 + 8283504041890 z^6 - 11228752776400 z^7 + 8213605202400 z^8 - 3152489683200 z^9 + 500824896000 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-14275149824 + 25371848320 z + 13472259775 z^2 + 28822140880 z^3 + 139349126410 z^4 + 2309740907452 z^5 - 12836768138945 z^6 + 27233627069980 z^7 - 30777686903600 z^8 + 19772246956800 z^9 - 6855886752000 z^10 + 1001649792000 z^11) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (1385566795817088885 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]