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

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=-21/8, b>=a

For fixed z and a=-21/8, b=31/8

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

Input Form

Hypergeometric2F1[-(21/8), 31/8, 23/4, z] == (1/(8927703 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (-34320 + 61204 z + 5603 z^2 + 8450 z^3 + 29315 z^4 - 120684 z^5 + 113664 z^6 - 33792 z^7 + (1/Sqrt[1 - z]) (34320 - 78364 z + 20709 z^2 - 143 z^3 - 21905 z^4 + 417191 z^5 - 784224 z^6 + 547584 z^7 - 135168 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]