Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4sb)

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=-25/8

http://functions.wolfram.com/07.23.03.b4sb.01

Input Form

Hypergeometric2F1[-(47/8), -(25/8), 5/2, -z] == (16 (Sqrt[z] Sqrt[1 + z] (167555 + 758137974 z - 5726414163 z^2 + 8806828832 z^3 - 3043877107 z^4 + 77288190 z^5 + 3728675 z^6 + 150220 z^7) Cosh[ArcSinh[Sqrt[z]]/4] - (670220 + 46077625 z - 845704074 z^2 + 1439340263 z^3 + 1066528924 z^4 - 1188442633 z^5 + 79133750 z^6 + 3803785 z^7 + 150220 z^8) Sinh[ArcSinh[Sqrt[z]]/4]))/(11947740189 z^(3/2) 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]