Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b691)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-31/8

http://functions.wolfram.com/07.23.03.b691.01

Input Form

Hypergeometric2F1[-(45/8), -(31/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[1 - z] (-1089961984 + 25098929280 z - 311002231085 z^2 + 3040769576425 z^3 - 34298893809075 z^4 - 776091612469523 z^5 - 1735519317567665 z^6 - 1029788937473925 z^7 - 158327253557825 z^8 - 2697688279825 z^9 + 34076062482 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-1089961984 + 25098929280 z - 311002231085 z^2 + 3040769576425 z^3 - 34298893809075 z^4 - 776091612469523 z^5 - 1735519317567665 z^6 - 1029788937473925 z^7 - 158327253557825 z^8 - 2697688279825 z^9 + 34076062482 z^10) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-1089961984 + 25780155520 z - 326577298205 z^2 + 3232624739400 z^3 - 36168659428300 z^4 + 1101558430278712 z^5 + 5410249046499570 z^6 + 6195972106419320 z^7 + 2091982711942900 z^8 + 169213350440200 z^9 + 5679343747 z^10) EllipticK[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (-1089961984 + 25098929280 z - 311002231085 z^2 + 3040769576425 z^3 - 34298893809075 z^4 - 776091612469523 z^5 - 1735519317567665 z^6 - 1029788937473925 z^7 - 158327253557825 z^8 - 2697688279825 z^9 + 34076062482 z^10) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (486673165943935715745 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]