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

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=47/8

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

Input Form

Hypergeometric2F1[-(37/8), 47/8, -(3/2), -z] == (1/(34224 (1 + z)^(19/8))) ((34224 - 548297 z + 14192265 z^2 + 384567216 z^3 + 1960254208 z^4 + 3922575360 z^5 + 3427860480 z^6 + 1095761920 z^7) Cos[(3 ArcTan[Sqrt[z]])/4] - 2 Sqrt[z] (-12834 + 207483 z + 87988934 z^2 + 579139968 z^3 + 1305976320 z^4 + 1225523200 z^5 + 410910720 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]