Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7lr)

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=-9/8

http://functions.wolfram.com/07.23.03.b7lr.01

Input Form

Hypergeometric2F1[-(43/8), -(9/8), 6, z] == (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (-240943104 + 3816501120 z - 30477207051 z^2 + 175120121538 z^3 - 1009131168573 z^4 - 30713322245060 z^5 - 25019170084125 z^6 - 132664937790 z^7 + 17640292845 z^8 - 1946135520 z^9 + 114168600 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 12 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (7529472 - 113795028 z + 870264315 z^2 - 4847965254 z^3 - 1808679359025 z^4 - 1703504641370 z^5 - 31944301095 z^6 + 4270344750 z^7 - 477971235 z^8 + 28542150 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (30117888 - 472121424 z + 3733698987 z^2 - 21300273342 z^3 + 4531021578765 z^4 + 5890245126640 z^5 + 992089200165 z^6 - 60382162470 z^7 + 7867899795 z^8 - 826405020 z^9 + 45667440 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (-240943104 + 3816501120 z - 30477207051 z^2 + 175120121538 z^3 - 1009131168573 z^4 - 30713322245060 z^5 - 25019170084125 z^6 - 132664937790 z^7 + 17640292845 z^8 - 1946135520 z^9 + 114168600 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (5777915751878106375 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]