Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5hq)

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=29/8

http://functions.wolfram.com/07.23.03.b5hq.01

Input Form

Hypergeometric2F1[-(47/8), 29/8, 21/4, z] == (1/(20689636275 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-6970288 + 14878884 z + 8143173 z^2 + 28283284 z^3 + 513723630 z^4 - 2644369056 z^5 + 5382918853 z^6 - 5917991904 z^7 + 3727012608 z^8 - 1273057280 z^9 + 183828480 z^10 + (1/Sqrt[1 - z]) (6970288 - 18364028 z - 1575017 z^2 - 22787480 z^3 - 497906438 z^4 + 3552216976 z^5 - 9463350921 z^6 + 13778353356 z^7 - 12082920960 z^8 + 6411029504 z^9 - 1906769920 z^10 + 245104640 z^11)))

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]