Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b91f)

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=1

http://functions.wolfram.com/07.23.03.b91f.01

Input Form

Hypergeometric2F1[-(41/8), 1, 6, z] == -((1/(71565039 z^5)) (8 (32768 (-1 + (1 - z)^(1/8)) - 4096 (-81 + 80 (1 - z)^(1/8)) z + 2304 (-657 + 640 (1 - z)^(1/8)) z^2 - 480 (-8541 + 8192 (1 - z)^(1/8)) z^3 + 15 (-486837 + 458752 (1 - z)^(1/8)) z^4 - 8257536 (1 - z)^(1/8) z^5 + 6881280 (1 - z)^(1/8) z^6 - 3932160 (1 - z)^(1/8) z^7 + 1474560 (1 - z)^(1/8) z^8 - 327680 (1 - z)^(1/8) z^9 + 32768 (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]