Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b6bo)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-23/8

http://functions.wolfram.com/07.23.03.b6bo.01

Input Form

Hypergeometric2F1[-(45/8), -(23/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-9888768 + 212711520 z - 2647965495 z^2 + 32813230590 z^3 + 722296936799 z^4 + 1362182425480 z^5 + 543499774935 z^6 + 24988817590 z^7 - 941826655 z^8 + 30964164 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-9888768 + 212711520 z - 2647965495 z^2 + 32813230590 z^3 + 722296936799 z^4 + 1362182425480 z^5 + 543499774935 z^6 + 24988817590 z^7 - 941826655 z^8 + 30964164 z^9) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 2 (-4944384 + 109446000 z - 1389948105 z^2 + 17223436545 z^3 - 527900566793 z^4 - 2347823918855 z^5 - 2098808684195 z^6 - 406178507365 z^7 - 79253515 z^8 + 2580347 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-9888768 + 212711520 z - 2647965495 z^2 + 32813230590 z^3 + 722296936799 z^4 + 1362182425480 z^5 + 543499774935 z^6 + 24988817590 z^7 - 941826655 z^8 + 30964164 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (57601274227001505 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]