Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4t0)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-21/8

http://functions.wolfram.com/07.23.03.b4t0.01

Input Form

Hypergeometric2F1[-(47/8), -(21/8), 5, z] == (65536 2^(1/4) (2 Sqrt[1 - z] (-1338295296 + 28452715616 z - 348834597605 z^2 + 4234567583610 z^3 + 89626580190685 z^4 + 158908119691160 z^5 + 55219433982405 z^6 + 860164666530 z^7 - 50246320605 z^8 + 1996101900 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1338295296 + 28452715616 z - 348834597605 z^2 + 4234567583610 z^3 + 89626580190685 z^4 + 158908119691160 z^5 + 55219433982405 z^6 + 860164666530 z^7 - 50246320605 z^8 + 1996101900 z^9) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (-1338295296 + 28452715616 z - 348834597605 z^2 + 4234567583610 z^3 + 89626580190685 z^4 + 158908119691160 z^5 + 55219433982405 z^6 + 860164666530 z^7 - 50246320605 z^8 + 1996101900 z^9) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 (-334573824 + 7322287544 z - 91620079330 z^2 + 1112434004435 z^3 - 33349535445410 z^4 - 141757471138595 z^5 - 116725273036400 z^6 - 18093521509635 z^7 + 443777810190 z^8 - 25672088325 z^9 + 998050950 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (7222478699089078425 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^4)

Standard Form

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MathML Form

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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 33349535445410 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1112434004435 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 91620079330 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7322287544 </cn> <ci> z </ci> </apply> <cn type='integer'> -334573824 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <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> 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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]