Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4x9)

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=-11/8

http://functions.wolfram.com/07.23.03.b4x9.01

Input Form

Hypergeometric2F1[-(47/8), -(11/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-14275149824 + 242733309312 z - 2110576632177 z^2 + 13495975308634 z^3 - 89891406519915 z^4 - 1186274915284956 z^5 - 920445942403127 z^6 - 11640207870918 z^7 + 1541223704691 z^8 - 163956311640 z^9 + 9240073920 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-14275149824 + 242733309312 z - 2110576632177 z^2 + 13495975308634 z^3 - 89891406519915 z^4 - 1186274915284956 z^5 - 920445942403127 z^6 - 11640207870918 z^7 + 1541223704691 z^8 - 163956311640 z^9 + 9240073920 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-14275149824 + 242733309312 z - 2110576632177 z^2 + 13495975308634 z^3 - 89891406519915 z^4 - 1186274915284956 z^5 - 920445942403127 z^6 - 11640207870918 z^7 + 1541223704691 z^8 - 163956311640 z^9 + 9240073920 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-14275149824 + 248086490496 z - 2200137862689 z^2 + 14263329522481 z^3 - 94748694405729 z^4 + 1304883996339609 z^5 + 2651187652201669 z^6 + 560492666280459 z^7 - 49447046948211 z^8 + 6475214176299 z^9 - 673535388240 z^10 + 36960295680 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (644540481290549438595 Pi (1 + Sqrt[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]