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

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=-33/8, b>=a

For fixed z and a=-33/8, b=35/8

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

Input Form

Hypergeometric2F1[-(33/8), 35/8, 19/4, z] == (8 2^(3/4) (-3740 - 7395 z - 22950 z^2 + 4504693 z^3 - 16004304 z^4 + 21958272 z^5 - 13604864 z^6 + 3194880 z^7 + (1/Sqrt[1 - z]) (3740 + 5525 z + 18785 z^2 + 4794543 z^3 - 23527713 z^4 + 45816288 z^5 - 44629760 z^6 + 21778432 z^7 - 4259840 z^8)))/ (74494953 (1 + Sqrt[1 - z])^(3/4) 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]