Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa8s)

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=-17/4, b>=a

For fixed z and a=-17/4, b=-15/4

http://functions.wolfram.com/07.23.03.aa8s.01

Input Form

Hypergeometric2F1[-(17/4), -(15/4), 6, -z] == (1/(1168766256232575 Pi z^5)) (16384 (1 + z)^(1/4) (2 (-452608 - 9073376 z - 95921735 z^2 - 778597365 z^3 - 7011599595 z^4 + 216670023759 z^5 - 432855081477 z^6 + 212285955825 z^7 - 24893250825 z^8 + 328582485 z^9) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (452608 + 8733920 z + 89424335 z^2 + 712532730 z^3 + 6487305825 z^4 - 78784080564 z^5 + 104785375905 z^6 - 32111978310 z^7 + 1800948495 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-452608 - 9073376 z - 95921735 z^2 - 778597365 z^3 - 7011599595 z^4 + 216670023759 z^5 - 432855081477 z^6 + 212285955825 z^7 - 24893250825 z^8 + 328582485 z^9) 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]