Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5bk)

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.b5bk.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, -(23/4), z] == (1/(1538240 2^(3/4) (-1 + z)^2)) ((1 + Sqrt[1 - z])^(3/4) (769120 + 668800 z + 646690 z^2 + 678546 z^3 + 790896 z^4 + 1119360 z^5 - 30210048 z^6 + 24330240 z^7 + (1/Sqrt[1 - z]) (769120 + 284240 z + 216150 z^2 + 223531 z^3 + 298943 z^4 + 551520 z^5 + 34814208 z^6 - 67989504 z^7 + 32440320 z^8)))

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]