Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bn2a)

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=-19/8, b>=a

For fixed z and a=-19/8, b=41/8

http://functions.wolfram.com/07.23.03.bn2a.01

Input Form

Hypergeometric2F1[-(19/8), 41/8, -(5/2), -z] == (1/(81600 (1 + z)^(37/8))) (-4 (-20400 + 20910 z - 7055 z^2 - 103275 z^3 + 491540 z^4 + 1461600 z^5 + 1279488 z^6 + 372736 z^7) Cos[(5 ArcTan[Sqrt[z]])/4] + Sqrt[z] (102000 - 85425 z + 16150 z^2 + 3870223 z^3 + 8516256 z^4 + 6746880 z^5 + 1863680 z^6) Sin[(5 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]