Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5612)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-13/3, b>=a

For fixed z and a=-13/3, b=6

http://functions.wolfram.com/07.23.03.5612.01

Input Form

Hypergeometric2F1[-(13/3), 6, -(7/3), -z] == (1/91854) (-((1/(1 + z)^4) (3 (-30618 + 218700 z - 1804275 z^2 + 45708300 z^3 + 407633600 z^4 + 1141574720 z^5 + 1466364900 z^6 + 897696800 z^7 + 213012800 z^8))) + 7607600 z^(10/3) (13 + 28 z) Log[1 + z^(1/3)] - 7607600 (-1)^(1/3) z^(10/3) (13 + 28 z) Log[1 - (-1)^(1/3) z^(1/3)] + 7607600 (-1)^(2/3) z^(10/3) (13 + 28 z) Log[1 + (-1)^(2/3) z^(1/3)])

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]