Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9c6)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=-1/4

http://functions.wolfram.com/07.23.03.a9c6.01

Input Form

Hypergeometric2F1[-(19/4), -(1/4), 6, z] == (1/(25488471943935 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 5397216 z + 32965779 z^2 - 136680775 z^3 + 517506990 z^4 + 3559913994 z^5 + 70835583 z^6 - 15241707 z^7 + 2386800 z^8 - 185640 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 5076192 z - 5076192 z^(3/2) - 29208795 z^2 + 29208795 z^(5/2) + 115350235 z^3 - 115350235 z^(7/2) - 434203770 z^4 + 434203770 z^(9/2) - 761838714 z^5 + 761838714 z^(11/2) + 121635969 z^6 - 121635969 z^(13/2) - 27139905 z^7 + 27139905 z^(15/2) + 4495140 z^8 - 4495140 z^(17/2) - 371280 z^9 + 371280 z^(19/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

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]