Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b95a)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-41/8, b>=a

For fixed z and a=-41/8, b=2

http://functions.wolfram.com/07.23.03.b95a.01

Input Form

Hypergeometric2F1[-(41/8), 2, 6, z] == -((1/(71565039 z^5)) (256 (-4096 (-1 + (1 - z)^(1/8)) + 128 (-243 + 239 (1 - z)^(1/8)) z - 144 (-657 + 632 (1 - z)^(1/8)) z^2 + 3 (-42705 + 39424 (1 - z)^(1/8)) z^3 + 10752 (1 - z)^(1/8) z^4 - 274176 (1 - z)^(1/8) z^5 + 446208 (1 - z)^(1/8) z^6 - 379392 (1 - z)^(1/8) z^7 + 188928 (1 - z)^(1/8) z^8 - 52352 (1 - z)^(1/8) z^9 + 6272 (1 - z)^(1/8) z^10)))

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]