Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7tb)

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.b7tb.01

Input Form

Hypergeometric2F1[-(43/8), 9/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (2650374144 - 25768676736 z + 111484193337 z^2 - 279127637415 z^3 + 423871405650 z^4 - 709226431814 z^5 + 640341818421 z^6 - 381352712307 z^7 + 146841608480 z^8 - 33252038400 z^9 + 3373117440 z^10) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (2650374144 - 26762567040 z + 120875680233 z^2 - 318436290117 z^3 + 518422014990 z^4 - 200580745034 z^5 + 175123555605 z^6 - 101528206113 z^7 + 38193986852 z^8 - 8471124480 z^9 + 843279360 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (2650374144 - 25768676736 z + 111484193337 z^2 - 279127637415 z^3 + 423871405650 z^4 - 709226431814 z^5 + 640341818421 z^6 - 381352712307 z^7 + 146841608480 z^8 - 33252038400 z^9 + 3373117440 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (2650374144 - 25768676736 z + 111484193337 z^2 - 279127637415 z^3 + 423871405650 z^4 - 709226431814 z^5 + 640341818421 z^6 - 381352712307 z^7 + 146841608480 z^8 - 33252038400 z^9 + 3373117440 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (168872880962864925 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]