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

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=-7/8, b>=a

For fixed z and a=-7/8, b=47/8

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

Input Form

Hypergeometric2F1[-(7/8), 47/8, -(11/2), -z] == (1/(289124352 (1 + z)^(21/2))) ((-Sqrt[1 + z]) (-289124352 - 2630045952 z - 10361407264 z^2 - 22550670597 z^3 - 27471545621 z^4 - 12113785866 z^5 + 21303554454 z^6 + 35526282119 z^7 + 27321548991 z^8 + 12186078168 z^9 + 3039130864 z^10 + 330106304 z^11) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-72281088 - 680099328 z - 2786224324 z^2 - 6365420867 z^3 - 8332747579 z^4 - 4594884294 z^5 + 36303442070 z^6 + 47840847745 z^7 + 33055328361 z^8 + 13664380312 z^9 + 3204184016 z^10 + 330106304 z^11) 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]