Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b69t)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-27/8

http://functions.wolfram.com/07.23.03.b69t.01

Input Form

Hypergeometric2F1[-(45/8), -(27/8), 5/2, z] == (1/(121755445 z^(3/2))) (16 (Sqrt[z] (-28971 + 9620182 z + 103559211 z^2 + 233761728 z^3 + 136884091 z^4 + 15593310 z^5 - 275931 z^6 + 8556 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((38628 - 2713617 z - 55888530 z^2 - 117706687 z^3 + 54594116 z^4 + 106217537 z^5 + 15730206 z^6 - 280209 z^7 + 8556 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]