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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-70090752 - 131146368 z - 310258385 z^2 - 1015019670 z^3 - 5955435885 z^4 + 97751523716 z^5 - 277423888896 z^6 + 336296125440 z^7 - 190997790720 z^8 + 41912893440 z^9) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-70090752 - 131146368 z - 310258385 z^2 - 1015019670 z^3 - 5955435885 z^4 + 97751523716 z^5 - 277423888896 z^6 + 336296125440 z^7 - 190997790720 z^8 + 41912893440 z^9) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (-70090752 - 131146368 z - 310258385 z^2 - 1015019670 z^3 - 5955435885 z^4 + 97751523716 z^5 - 277423888896 z^6 + 336296125440 z^7 - 190997790720 z^8 + 41912893440 z^9) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (-70090752 - 104862336 z - 253891457 z^2 - 881407035 z^3 - 5533347015 z^4 - 142480154509 z^5 + 814276896048 z^6 - 1681830399744 z^7 + 1693436067840 z^8 - 844324208640 z^9 + 167651573760 z^10) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/(63594152067451005 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]