Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8554)

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=10/3, b>=a

For fixed z and a=10/3, b=11/3

http://functions.wolfram.com/07.23.03.8554.01

Input Form

Hypergeometric2F1[10/3, 11/3, -(9/2), z] == (1/(26873856 (-1 + z)^11)) ((1/Sqrt[1 - z]) (9 (-2985984 + 42614784 z - 299278336 z^2 + 1440137216 z^3 - 6002470912 z^4 + 38181535744 z^5 + 128796310969 z^6 + 55305361948 z^7 + 3459329712 z^8) Cos[ArcSin[Sqrt[z]]/3]) - Sqrt[z] (8957952 - 121540608 z + 812994560 z^2 - 3757305856 z^3 + 15421497344 z^4 + 369374503555 z^5 + 257579880124 z^6 + 23442678352 z^7) Sin[ArcSin[Sqrt[z]]/3])

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]