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

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=21/8

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

Input Form

Hypergeometric2F1[-(37/8), 21/8, -(11/2), z] == (1/(135168 (-1 + z)^3)) ((-135168 + 145152 z + 34720 z^2 + 25067 z^3 + 24741 z^4 + 33696 z^5 + 106080 z^6 - 411264 z^7 + 228480 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) (4 Sqrt[z] (-25344 + 30912 z + 4851 z^2 + 2918 z^3 + 2853 z^4 + 4446 z^5 + 70788 z^6 - 131376 z^7 + 57120 z^8) Sin[(3 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]