Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7bw)

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=-45/8, b>=a

For fixed z and a=-45/8, b=47/8

http://functions.wolfram.com/07.23.03.b7bw.01

Input Form

Hypergeometric2F1[-(45/8), 47/8, 5/2, z] == (1/(121755445 z^(3/2))) (8 ((1 - Sqrt[z])^(9/4) (-38628 - 86913 Sqrt[z] - 2549448 z + 1991152 z^(3/2) + 87337152 z^2 + 92816640 z^(5/2) - 489431040 z^3 - 764559360 z^(7/2) + 731971584 z^4 + 1701249024 z^(9/2) + 80216064 z^5 - 1123024896 z^(11/2) - 499122176 z^6) + (1 + Sqrt[z])^(9/4) (38628 - 86913 Sqrt[z] + 2549448 z + 1991152 z^(3/2) - 87337152 z^2 + 92816640 z^(5/2) + 489431040 z^3 - 764559360 z^(7/2) - 731971584 z^4 + 1701249024 z^(9/2) - 80216064 z^5 - 1123024896 z^(11/2) + 499122176 z^6)))

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]