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

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=-37/8, b>=a

For fixed z and a=-37/8, b=-23/8

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

Input Form

Hypergeometric2F1[-(37/8), -(23/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-35160064 + 647027584 z - 6234768435 z^2 + 45825061660 z^3 - 372570348745 z^4 - 5094129682110 z^5 - 6336327906405 z^6 - 1609008005880 z^7 - 40988812095 z^8 + 696693690 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-35160064 + 647027584 z - 6234768435 z^2 + 45825061660 z^3 - 372570348745 z^4 - 5094129682110 z^5 - 6336327906405 z^6 - 1609008005880 z^7 - 40988812095 z^8 + 696693690 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-35160064 + 669002624 z - 6635555395 z^2 + 49657136305 z^3 - 400601776295 z^4 + 8977389057805 z^5 + 26913062334375 z^6 + 16125693705315 z^7 + 1989188742915 z^8 + 116115615 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-35160064 + 647027584 z - 6234768435 z^2 + 45825061660 z^3 - 372570348745 z^4 - 5094129682110 z^5 - 6336327906405 z^6 - 1609008005880 z^7 - 40988812095 z^8 + 696693690 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (3628880276301094815 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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]