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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=-16/5, b>=a

For fixed z and a=-16/5, b=6

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

Input Form

Hypergeometric2F1[-(16/5), 6, 19/5, -z] == (1/(6103515625 z^(14/5))) (21 (-1)^(1/5) (528 (-1)^(4/5) (33 - 352 z + 4620 z^2 + 160160 z^3 + 620620 z^4 + 812448 z^5 + 346983 z^6) Log[1 + z^(1/5)] + 528 (33 - 352 z + 4620 z^2 + 160160 z^3 + 620620 z^4 + 812448 z^5 + 346983 z^6) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (528 (33 - 352 z + 4620 z^2 + 160160 z^3 + 620620 z^4 + 812448 z^5 + 346983 z^6) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-528 (33 - 352 z + 4620 z^2 + 160160 z^3 + 620620 z^4 + 812448 z^5 + 346983 z^6) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-4356 + 48400 z + 57496985 z^2 + 272847120 z^3 + 398438040 z^4 + 183207024 z^5) + 528 (33 - 352 z + 4620 z^2 + 160160 z^3 + 620620 z^4 + 812448 z^5 + 346983 z^6) Log[1 + (-1)^(4/5) z^(1/5)])))))

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]