Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b59f)

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=-47/8, b>=a

For fixed z and a=-47/8, b=15/8

http://functions.wolfram.com/07.23.03.b59f.01

Input Form

Hypergeometric2F1[-(47/8), 15/8, 11/2, z] == (1/(751899556815 z^(9/2))) (1024 (4 Sqrt[z] (-536176 + 4088342 z - 12097471 z^2 + 13069290 z^3 + 205596746 z^4 - 441281650 z^5 + 498236937 z^6 - 348003238 z^7 + 151303460 z^8 - 37763792 z^9 + 4153248 z^10) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((8578816 - 71311408 z + 237827567 z^2 - 337154171 z^3 - 222177930 z^4 + 1522981178 z^5 - 2619978389 z^6 + 2622094497 z^7 - 1676776288 z^8 + 678664800 z^9 - 159361664 z^10 + 16612992 z^11) 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]