Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cdm1)

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=41/8, b>=a

For fixed z and a=41/8, b=45/8

http://functions.wolfram.com/07.23.03.cdm1.01

Input Form

Hypergeometric2F1[41/8, 45/8, -(11/2), -z] == (1/(45056 (1 + z)^(129/8))) ((45056 + 961280 z + 10338080 z^2 + 77042079 z^3 + 475550520 z^4 + 2995130788 z^5 + 34755423560 z^6 - 212823814470 z^7 + 244751266440 z^8 - 80965811420 z^9 + 6906420568 z^10 - 69525665 z^11) Cos[ArcTan[Sqrt[z]]/4] - 4 Sqrt[z] (-2816 - 59200 z - 627861 z^2 - 4623660 z^3 - 28326080 z^4 - 178697948 z^5 + 28632780910 z^6 - 67156586820 z^7 + 41061820920 z^8 - 7160929780 z^9 + 254722927 z^10) Sin[ArcTan[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]