Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bf0q)

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=-31/8, b>=a

For fixed z and a=-31/8, b=-1/8

http://functions.wolfram.com/07.23.03.bf0q.01

Input Form

Hypergeometric2F1[-(31/8), -(1/8), 11/2, -z] == -((1024 (4 Sqrt[z] Sqrt[1 + z] (-399280 - 4356430 z - 22964304 z^2 - 84462693 z^3 - 6541598602 z^4 + 824943860 z^5 + 155112880 z^6 + 25484823 z^7 + 2148146 z^8) Cosh[ArcSinh[Sqrt[z]]/4] + (6388480 + 74094960 z + 414825539 z^2 + 1598545287 z^3 + 6844924062 z^4 + 2568406102 z^5 - 3597795825 z^6 - 670347093 z^7 - 106235584 z^8 - 8592584 z^9) Sinh[ArcSinh[Sqrt[z]]/4]))/ (25272884139789 z^(9/2) Sqrt[1 + z]))

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]