Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7rm)

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=-23/4, b>=a

For fixed z and a=-23/4, b=5

http://functions.wolfram.com/07.23.03.a7rm.01

Input Form

Hypergeometric2F1[-(23/4), 5, -(15/4), z] == (1/(540672 (-1 + z)^3)) (-2 (270336 + 1261568 z + 5332992 z^2 + 27426816 z^3 + 262840320 z^4 - 2753874801 z^5 + 6413759415 z^6 - 5787075195 z^7 + 1830673845 z^8) + 140821065 (-1 + z)^3 z^(19/4) (-23 + 39 z) ArcTan[z^(1/4)] + 140821065 (-1 + z)^3 z^(19/4) (-23 + 39 z) 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]