Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5mr)

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=37/8

http://functions.wolfram.com/07.23.03.b5mr.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (51472896 + 122784304 z + 427432805 z^2 + 2786774760 z^3 - 55521683455 z^4 + 196024310482 z^5 - 315507088512 z^6 + 267909818880 z^7 - 117282570240 z^8 + 20956446720 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (51472896 + 122784304 z + 427432805 z^2 + 2786774760 z^3 - 55521683455 z^4 + 196024310482 z^5 - 315507088512 z^6 + 267909818880 z^7 - 117282570240 z^8 + 20956446720 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[1 - z] (51472896 + 122784304 z + 427432805 z^2 + 2786774760 z^3 - 55521683455 z^4 + 196024310482 z^5 - 315507088512 z^6 + 267909818880 z^7 - 117282570240 z^8 + 20956446720 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (102945792 + 206963936 z + 752221417 z^2 + 5222186685 z^3 + 149023942795 z^4 - 1012659411841 z^5 + 2593468552752 z^6 - 3460080366336 z^7 + 2575034204160 z^8 - 1018593607680 z^9 + 167651573760 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(8593804333439325 Pi (1 + Sqrt[1 - z])^(1/4) 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]