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

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=-35/8, b>=a

For fixed z and a=-35/8, b=-31/8

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

Input Form

Hypergeometric2F1[-(35/8), -(31/8), 11/2, -z] == -((1024 (Sqrt[z] (-11200 - 238200 z - 2770125 z^2 - 26992875 z^3 - 1772270929 z^4 + 7972602105 z^5 - 8920193415 z^6 + 3037968255 z^7 - 271823835 z^8 + 2889643 z^9) Cos[(5 ArcTan[Sqrt[z]])/4] + (8960 + 188880 z + 2180643 z^2 + 21184485 z^3 + 336558495 z^4 - 4635640295 z^5 + 9808107465 z^6 - 6051694929 z^7 + 1099290165 z^8 - 41190845 z^9) Sin[(5 ArcTan[Sqrt[z]])/4]))/ (1378911632813 z^(9/2) (1 + z)^(5/8)))

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]