Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bd09)

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=-35/8, b>=a

For fixed z and a=-35/8, b=25/8

http://functions.wolfram.com/07.23.03.bd09.01

Input Form

Hypergeometric2F1[-(35/8), 25/8, -(19/4), z] == (-10336 + 1904 z + 3162 z^2 + 5185 z^3 + 10149 z^4 + 34272 z^5 - 102144 z^6 + 53248 z^7 + (1/Sqrt[1 - z]) (2 (-5168 + 3536 z + 1751 z^2 + 2006 z^3 + 3723 z^4 + 14280 z^5 - 200256 z^6 + 277504 z^7 - 106496 z^8)))/ (10336 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + 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]