Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.blm8)

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=-21/8, b>=a

For fixed z and a=-21/8, b=15/8

http://functions.wolfram.com/07.23.03.blm8.01

Input Form

Hypergeometric2F1[-(21/8), 15/8, 9/2, -z] == (1/(805035 z^(7/2) (1 + z)^(3/8))) (256 (Sqrt[z] (-720 - 2829 z - 2925 z^2 + 6413 z^3 + 10317 z^4 + 6000 z^5 + 1280 z^6) Cos[(3 ArcTan[Sqrt[z]])/4] - 2 (-480 - 1956 z - 2209 z^2 + 1950 z^3 + 3567 z^4 + 2180 z^5 + 480 z^6) 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]