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

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=-37/8, b>=a

For fixed z and a=-37/8, b=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(11/2), -z] == (1/(289124352 (1 + z)^(51/8))) ((-(-289124352 - 333478656 z + 255698912 z^2 - 271834815 z^3 + 356962737 z^4 - 703526369 z^5 + 4165293951 z^6 + 49212648144 z^7 + 114627034368 z^8 + 117776203776 z^9 + 57905971200 z^10 + 11176771584 z^11)) Cos[(3 ArcTan[Sqrt[z]])/4] + 2 Sqrt[z] (108421632 + 109243008 z - 108194898 z^2 + 119663503 z^3 - 155629362 z^4 + 292557447 z^5 + 14055113226 z^6 + 37612054656 z^7 + 41228554752 z^8 + 21103509504 z^9 + 4191289344 z^10) Sin[(3 ArcTan[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]