Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7uy)

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=15/8

http://functions.wolfram.com/07.23.03.b7uy.01

Input Form

Hypergeometric2F1[-(43/8), 15/8, 6, z] == (1/(20132110633721625 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (883458048 - 7119429504 z + 23456582259 z^2 - 36342430443 z^3 + 7218807750 z^4 - 32574719830 z^5 + 43657327615 z^6 - 33245181215 z^7 + 15282123480 z^8 - 3971900400 z^9 + 450840000 z^10) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-110432256 + 809692752 z - 2351565381 z^2 + 2887523100 z^3 - 24543946350 z^4 + 36376004660 z^5 - 29446585445 z^6 + 14188986760 z^7 - 3836648400 z^8 + 450840000 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 20 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-27608064 + 217952724 z - 698640393 z^2 + 1031258250 z^3 + 3753780030 z^4 - 7509256660 z^5 + 7690522135 z^6 - 4883076770 z^7 + 1939739100 z^8 - 444528240 z^9 + 45084000 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (883458048 - 7119429504 z + 23456582259 z^2 - 36342430443 z^3 + 7218807750 z^4 - 32574719830 z^5 + 43657327615 z^6 - 33245181215 z^7 + 15282123480 z^8 - 3971900400 z^9 + 450840000 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))

Standard Form

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MathML Form

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type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15282123480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33245181215 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 43657327615 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32574719830 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7218807750 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 36342430443 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> 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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]