Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9k4)

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=9/4

http://functions.wolfram.com/07.23.03.a9k4.01

Input Form

Hypergeometric2F1[-(19/4), 9/4, 5, z] == (1/(4928737275 Pi z^4)) (4096 (2 Sqrt[1 - z] (-80256 + 364496 z - 399399 z^2 - 522291 z^3 + 2964395 z^4 - 4411617 z^5 + 3276672 z^6 - 1251328 z^7 + 196608 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 8 (-10032 + 53086 z - 83391 z^2 - 30723 z^3 + 120925 z^4 - 162099 z^5 + 112602 z^6 - 40832 z^7 + 6144 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-80256 + 364496 z - 399399 z^2 - 522291 z^3 + 2964395 z^4 - 4411617 z^5 + 3276672 z^6 - 1251328 z^7 + 196608 z^8) EllipticK[(1/2) (1 - Sqrt[1 - 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]