Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8vx)

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=5

http://functions.wolfram.com/07.23.03.a8vx.01

Input Form

Hypergeometric2F1[-(21/4), 5, -(9/4), z] == (1/(393216 (-1 + z)^2)) (2 (196608 + 1900544 z + 19005440 z^2 + 665190400 z^3 - 5253716125 z^4 + 12517001315 z^5 - 12058501455 z^6 + 4108329225 z^7) + 10094175 (-1 + z)^2 z^(13/4) (119 - 462 z + 407 z^2) ArcTan[z^(1/4)] - 10094175 (-1 + z)^2 z^(13/4) (119 - 462 z + 407 z^2) ArcTanh[z^(1/4)])

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]