Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa8k)

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.aa8k.01

Input Form

Hypergeometric2F1[-(17/4), -(15/4), 4, -z] == (1/(145568097675 Pi z^3)) (256 (1 + z)^(1/4) (2 (-77792 - 1888887 z - 33854106 z^2 + 1851174615 z^3 - 5537951820 z^4 + 3789439911 z^5 - 590556954 z^6 + 9993753 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (77792 + 1830543 z + 32490315 z^2 - 738080490 z^3 + 1492929270 z^4 - 642924981 z^5 + 48117711 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-77792 - 1888887 z - 33854106 z^2 + 1851174615 z^3 - 5537951820 z^4 + 3789439911 z^5 - 590556954 z^6 + 9993753 z^7) 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]