Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bl4s)

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=-19/8

http://functions.wolfram.com/07.23.03.bl4s.01

Input Form

Hypergeometric2F1[-(21/8), -(19/8), 9/2, z] == (1/(2452502535 z^(7/2))) (256 (Sqrt[z] (-4560 + 65303 z - 541975 z^2 + 15367094 z^3 + 37153714 z^4 + 14170435 z^5 + 636709 z^6) Cos[(3 ArcSin[Sqrt[z]])/4] + (1/Sqrt[1 - z]) ((6080 - 92264 z + 796803 z^2 - 8330455 z^3 - 21681122 z^4 + 16092906 z^5 + 12571343 z^6 + 636709 z^7) Sin[(3 ArcSin[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]