Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bms9)

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=25/8

http://functions.wolfram.com/07.23.03.bms9.01

Input Form

Hypergeometric2F1[-(19/8), 25/8, -(19/4), z] == (-544 + 1904 z - 1938 z^2 + 85 z^3 + 204 z^4 + 561 z^5 - 784 z^6 + 256 z^7 + (2 (-272 + 1088 z - 1411 z^2 + 425 z^3 + 153 z^4 + 255 z^5 - 2158 z^6 + 1920 z^7 - 512 z^8))/Sqrt[1 - z])/(544 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]