Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b54x)

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=7/8

http://functions.wolfram.com/07.23.03.b54x.01

Input Form

Hypergeometric2F1[-(47/8), 7/8, 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (15012928 + 158976184 z + 769848203 z^2 + 2287896503 z^3 + 26502288406 z^4 + 25134514774 z^5 + 18222732871 z^6 + 9373211771 z^7 + 3224970056 z^8 + 665934192 z^9 + 62452544 z^10) Cosh[ArcSinh[Sqrt[z]]/4] - (60051712 + 677190288 z + 3511651201 z^2 + 11218879602 z^3 + 26895828067 z^4 + 37268482900 z^5 + 33251484999 z^6 + 22545398834 z^7 + 10906358309 z^8 + 3550130584 z^9 + 697160464 z^10 + 62452544 z^11) Sinh[ArcSinh[Sqrt[z]]/4]))/ (21805087147635 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]