Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5bo)

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=-47/8, b>=a

For fixed z and a=-47/8, b=21/8

http://functions.wolfram.com/07.23.03.b5bo.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, -(19/4), z] == (1/(33440 2^(3/4) (-1 + z))) ((1 + Sqrt[1 - z])^(3/4) (-16720 - 40700 z - 82137 z^2 - 167952 z^3 - 401280 z^4 + 24938496 z^5 - 24330240 z^6 + (1/Sqrt[1 - z]) (-16720 - 32340 z - 59697 z^2 - 120751 z^3 - 303840 z^4 - 27853056 z^5 + 60960768 z^6 - 32440320 z^7)))

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]