Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8758)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=13/3, b>=a

For fixed z and a=13/3, b=14/3

http://functions.wolfram.com/07.23.03.8758.01

Input Form

Hypergeometric2F1[13/3, 14/3, -(11/2), z] == ((1/Sqrt[1 - z]) ((7094697984 - 129352826880 z + 1167266709504 z^2 - 7131012235264 z^3 + 34990538260480 z^4 - 167842161721344 z^5 + 1390757167923200 z^6 + 7004769984002413 z^7 + 5713767443559504 z^8 + 1142092224185024 z^9 + 40993776737344 z^10) Cos[ArcSin[Sqrt[z]]/3]) - 9 Sqrt[z] (-262766592 + 4605935616 z - 40011071488 z^2 + 236299616256 z^3 - 1132568346624 z^4 + 5436141928448 z^5 + 209461576580559 z^6 + 269416687219800 z^7 + 74273039188256 z^8 + 3583120208064 z^9) Sin[ArcSin[Sqrt[z]]/3])/(7094697984 (-1 + z)^14)

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]