Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8za)

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=6

http://functions.wolfram.com/07.23.03.a8za.01

Input Form

Hypergeometric2F1[-(21/4), 6, -(13/4), z] == (1/(12779520 (-1 + z)^4)) (2 (6389760 + 36372480 z + 200048640 z^2 + 1547042816 z^3 + 48345088000 z^4 - 377340434625 z^5 + 991757697700 z^6 - 1222456184950 z^7 + 726352606980 z^8 - 168441498225 z^9) - 4108329225 (-1 + z)^4 z^(17/4) (-21 + 41 z) ArcTan[z^(1/4)] + 4108329225 (-1 + z)^4 z^(17/4) (-21 + 41 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]