Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7o8)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-1/8

http://functions.wolfram.com/07.23.03.b7o8.01

Input Form

Hypergeometric2F1[-(43/8), -(1/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (562200576 - 7446961536 z + 47827728207 z^2 - 207979041270 z^3 + 814145442033 z^4 + 12129321328440 z^5 + 217957827985 z^6 - 62475532270 z^7 + 15040406175 z^8 - 2404608180 z^9 + 184844400 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-70275072 + 879810960 z - 5344182459 z^2 + 22174101411 z^3 + 3062708937750 z^4 + 202095087270 z^5 - 58455142175 z^6 + 14359381415 z^7 - 2349154860 z^8 + 184844400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-35137536 + 459670344 z - 2915574795 z^2 + 12542418966 z^3 - 993574995105 z^4 - 354747977700 z^5 + 56369286035 z^6 - 15596803850 z^7 + 3508520265 z^8 - 519738960 z^9 + 36968880 z^10) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 2 (562200576 - 7446961536 z + 47827728207 z^2 - 207979041270 z^3 + 814145442033 z^4 + 12129321328440 z^5 + 217957827985 z^6 - 62475532270 z^7 + 15040406175 z^8 - 2404608180 z^9 + 184844400 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (2476249607947759875 Pi 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]