Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bh77)

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=-29/8, b>=a

For fixed z and a=-29/8, b=39/8

http://functions.wolfram.com/07.23.03.bh77.01

Input Form

Hypergeometric2F1[-(29/8), 39/8, 23/4, z] == (1/(18542839131 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (6966960 + 1509508 z + 2662751 z^2 + 7264790 z^3 + 41777255 z^4 - 325146768 z^5 + 576225408 z^6 - 410302464 z^7 + 105431040 z^8 + (1/Sqrt[1 - z]) (-6966960 + 1973972 z - 1037127 z^2 - 5309291 z^3 - 37445525 z^4 + 926823107 z^5 - 2767255968 z^6 + 3398638848 z^7 - 1931145216 z^8 + 421724160 z^9)))

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]