Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5j2)

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=31/8

http://functions.wolfram.com/07.23.03.b5j2.01

Input Form

Hypergeometric2F1[-(47/8), 31/8, 11/2, z] == (1/(3759497784075 z^(9/2))) (1024 (2 Sqrt[z] (-4242784 + 7197580 z + 6458881 z^2 + 15380092 z^3 + 1962361038 z^4 - 8700993664 z^5 + 16737561225 z^6 - 17797145872 z^7 + 10947751056 z^8 - 3672193536 z^9 + 522466560 z^10) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((33942272 - 80915952 z - 14868685 z^2 - 84135922 z^3 - 923070694 z^4 + 9990069408 z^5 - 30800413237 z^6 + 48953537050 z^7 - 45689302736 z^8 + 25437079008 z^9 - 7866853632 z^10 + 1044933120 z^11) Sin[ArcSin[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]