Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab5e)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-9/4

http://functions.wolfram.com/07.23.03.ab5e.01

Input Form

Hypergeometric2F1[-(15/4), -(9/4), 6, -z] == (1/(31588277195475 Pi z^5)) (16384 (1 + z)^(1/4) (-2 (67584 + 1059168 z + 8458835 z^2 + 49588770 z^3 + 303458925 z^4 - 5352158532 z^5 + 5324945661 z^6 - 872237790 z^7 + 480675 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + (67584 + 1059168 z + 8458835 z^2 + 49588770 z^3 + 303458925 z^4 - 5352158532 z^5 + 5324945661 z^6 - 872237790 z^7 + 480675 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - Sqrt[1 + z] (-67584 - 1008480 z - 7710395 z^2 - 43921185 z^3 - 271378800 z^4 + 1694871822 z^5 - 962645355 z^6 + 62007075 z^7 + 961350 z^8) EllipticK[1/2 - 1/(2 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]