Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ba3w)

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=-39/8, b>=a

For fixed z and a=-39/8, b=5/8

http://functions.wolfram.com/07.23.03.ba3w.01

Input Form

Hypergeometric2F1[-(39/8), 5/8, 21/4, z] == (1/(4444440385 z^5)) (16 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (444912 - 4611684 z + 22287667 z^2 - 70061519 z^3 + 265074862 z^4 - 105135730 z^5 + 55415375 z^6 - 20472811 z^7 + 4589424 z^8 - 467712 z^9 + (1/Sqrt[1 - z]) (-444912 + 4834140 z - 24537895 z^2 + 80656699 z^3 - 297590514 z^4 + 369029234 z^5 - 202481915 z^6 + 97009959 z^7 - 32503084 z^8 + 6651904 z^9 - 623616 z^10)))

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]