Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b9uz)

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=-39/8, b>=a

For fixed z and a=-39/8, b=-17/8

http://functions.wolfram.com/07.23.03.b9uz.01

Input Form

Hypergeometric2F1[-(39/8), -(17/8), 9/2, z] == (1/(343070825427 z^(7/2))) (256 (Sqrt[z] (-11408 + 213187 z - 2411366 z^2 + 1377408365 z^3 + 3314558160 z^4 + 1408335693 z^5 + 40192434 z^6 - 2108445 z^7 + 90132 z^8) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((45632 - 884120 z + 10227985 z^2 - 155714922 z^3 - 648658873 z^4 + 230829456 z^5 + 524982831 z^6 + 41235390 z^7 - 2153511 z^8 + 90132 z^9) Sin[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]