Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b67a)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-35/8

http://functions.wolfram.com/07.23.03.b67a.01

Input Form

Hypergeometric2F1[-(45/8), -(35/8), 7/2, z] == (1/(116902620835 z^(5/2))) (64 (-2 Sqrt[z] (-173826 + 6460533 z - 1183799501 z^2 - 11578234203 z^3 - 27512608425 z^4 - 20534403929 z^5 - 4594888143 z^6 - 202372929 z^7 + 1105863 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((463536 - 17624025 z + 736027569 z^2 + 12450341301 z^3 + 27277435669 z^4 - 5393399681 z^5 - 26427567725 z^6 - 8222036649 z^7 - 405851721 z^8 + 2211726 z^9) 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]