Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7544)

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=1/3, b>=a

For fixed z and a=1/3, b=14/3

http://functions.wolfram.com/07.23.03.7544.01

Input Form

Hypergeometric2F1[1/3, 14/3, -(11/2), z] == (1/(55427328 (-1 + z)^10)) ((1/Sqrt[1 - z]) ((55427328 - 600742656 z + 2974406400 z^2 - 8925340928 z^3 + 18251999744 z^4 - 27706629632 z^5 + 39774293504 z^6 - 4948282905 z^7 + 1465089512 z^8 - 281932896 z^9 + 25399360 z^10) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (18475776 - 187246080 z + 861122304 z^2 - 2382831616 z^3 + 4466767360 z^4 - 6247138304 z^5 - 4313525685 z^6 + 1333647824 z^7 - 269233216 z^8 + 25399360 z^9) 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]