Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8gl)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-1/4

http://functions.wolfram.com/07.23.03.a8gl.01

Input Form

Hypergeometric2F1[-(21/4), -(1/4), 6, z] == (1/(168441498225 Pi z^5)) (16384 (2 (2048 - 27424 z + 178851 z^2 - 796074 z^3 + 3243501 z^4 + 39741556 z^5 + 3243501 z^6 - 796074 z^7 + 178851 z^8 - 27424 z^9 + 2048 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-2048 + 26912 z - 172363 z^2 + 755987 z^3 - 3072838 z^4 - 19870778 z^5 - 170663 z^6 + 40087 z^7 - 6488 z^8 + 512 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (2048 - 27424 z + 178851 z^2 - 796074 z^3 + 3243501 z^4 + 39741556 z^5 + 3243501 z^6 - 796074 z^7 + 178851 z^8 - 27424 z^9 + 2048 z^10) 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]