Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b839)

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=31/8

http://functions.wolfram.com/07.23.03.b839.01

Input Form

Hypergeometric2F1[-(43/8), 31/8, 6, z] == (1/(16342536867374025 Pi z^5)) (262144 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-4 (883458048 - 2536490880 z + 398672307 z^2 + 600798924 z^3 + 2143561266 z^4 - 33145458540 z^5 + 87451432675 z^6 - 109497589560 z^7 + 74746460880 z^8 - 26991631680 z^9 + 4060742400 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 + 236825424 z + 114449445 z^2 + 20948697 z^3 - 21019469625 z^4 + 66699105555 z^5 - 92235838520 z^6 + 67535566800 z^7 - 25773408960 z^8 + 4060742400 z^9) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 10 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-55216128 + 149471784 z - 3154437 z^2 - 32029668 z^3 + 6097769370 z^4 - 23001026700 z^5 + 38935339955 z^6 - 36981662640 z^7 + 20518046640 z^8 - 6251082240 z^9 + 812148480 z^10) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 (883458048 - 2536490880 z + 398672307 z^2 + 600798924 z^3 + 2143561266 z^4 - 33145458540 z^5 + 87451432675 z^6 - 109497589560 z^7 + 74746460880 z^8 - 26991631680 z^9 + 4060742400 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'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4060742400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 26991631680 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> 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</math>

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]