Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4n5)

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=-41/8

http://functions.wolfram.com/07.23.03.b4n5.01

Input Form

Hypergeometric2F1[-(47/8), -(41/8), 3/2, -z] == (1/828425745) (4 ((208823875 - 4274199070 z + 17627853181 z^2 - 21042755492 z^3 + 7526739213 z^4 - 637833438 z^5 + 3299475 z^6) Cosh[ArcSinh[Sqrt[z]]/4] + (1/(Sqrt[z] Sqrt[1 + z])) ((-6869755 + 437264075 z - 2798584295 z^2 + 2589061191 z^3 + 2882212943 z^4 - 2597557311 z^5 + 348709587 z^6 - 3299475 z^7) Sinh[ArcSinh[Sqrt[z]]/4])))

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]