Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.cag9)

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=27/8, b>=a

For fixed z and a=27/8, b=39/8

http://functions.wolfram.com/07.23.03.cag9.01

Input Form

Hypergeometric2F1[27/8, 39/8, -(21/4), z] == (1/(236096 2^(1/4) (-1 + z)^13)) ((1 + Sqrt[1 - z])^(1/4) (-118048 + 1897200 z - 15019810 z^2 + 80501885 z^3 - 351510612 z^4 + 1601858071 z^5 + 24673598670 z^6 + 20926875915 z^7 + 2990665320 z^8 + 3469009 z^9 + (1/Sqrt[1 - z]) (2 (-59024 + 978112 z - 7976827 z^2 + 43891009 z^3 - 194999021 z^4 + 884209249 z^5 - 34036253859 z^6 - 51303440181 z^7 - 14673088263 z^8 - 544634413 z^9 + 6938018 z^10))))

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]