Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc2j)

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=31/8

http://functions.wolfram.com/07.23.03.bc2j.01

Input Form

Hypergeometric2F1[-(37/8), 31/8, 9/2, -z] == (256 (Sqrt[z] (-51504 + 65453 z - 209235 z^2 + 6122979 z^3 + 33889619 z^4 + 68340960 z^5 + 67491072 z^6 + 33116160 z^7 + 6488064 z^8) Cos[(3 ArcTan[Sqrt[z]])/4] - 2 (-34336 + 38628 z - 131979 z^2 + 1311206 z^3 + 10043517 z^4 + 22546584 z^5 + 23631168 z^6 + 12063744 z^7 + 2433024 z^8) Sin[(3 ArcTan[Sqrt[z]])/4]))/ (1055400885 z^(7/2) (1 + z)^(3/8))

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]