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

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=-19/8, b>=a

For fixed z and a=-19/8, b=17/8

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

Input Form

Hypergeometric2F1[-(19/8), 17/8, -(23/4), z] == (-1472 + 6160 z - 9192 z^2 + 5081 z^3 - 18 z^4 - 135 z^5 - 360 z^6 + 192 z^7 + (-1472 + 6896 z - 12088 z^2 + 8999 z^3 - 1737 z^4 - 387 z^5 - 387 z^6 + 1968 z^7 - 768 z^8)/Sqrt[1 - z])/ (1472 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-1 + z)^5)

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]