Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm6k)

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=-21/8, b>=a

For fixed z and a=-21/8, b=47/8

http://functions.wolfram.com/07.23.03.bm6k.01

Input Form

Hypergeometric2F1[-(21/8), 47/8, -(11/2), z] == (1/8380416) ((1/(1 - Sqrt[z])^(35/4)) (4190208 - 36664320 Sqrt[z] + 153823488 z - 422472960 z^(3/2) + 872478880 z^2 - 1460499404 z^(5/2) + 2062672885 z^3 - 2503713264 z^(7/2) + 2617436640 z^4 - 2323601280 z^(9/2) + 1692058368 z^5 - 953272320 z^(11/2) + 381308928 z^6 - 94617600 z^(13/2) + 10813440 z^7) + (1/(1 + Sqrt[z])^(35/4)) (4190208 + 36664320 Sqrt[z] + 153823488 z + 422472960 z^(3/2) + 872478880 z^2 + 1460499404 z^(5/2) + 2062672885 z^3 + 2503713264 z^(7/2) + 2617436640 z^4 + 2323601280 z^(9/2) + 1692058368 z^5 + 953272320 z^(11/2) + 381308928 z^6 + 94617600 z^(13/2) + 10813440 z^7))

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]