Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8s9)

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=-21/8

http://functions.wolfram.com/07.23.03.b8s9.01

Input Form

Hypergeometric2F1[-(41/8), -(21/8), 9/2, -z] == (256 (Sqrt[z] (560 + 11851 z + 154511 z^2 + 9358115 z^3 - 48457409 z^4 + 56437017 z^5 - 17051195 z^6 + 711529 z^7 + 22589 z^8 + 784 z^9) Cos[(7 ArcTan[Sqrt[z]])/4] - 2 (160 + 3276 z + 41825 z^2 + 773528 z^3 - 13304837 z^4 + 30824794 z^5 - 18573737 z^6 + 2506484 z^7 + 20237 z^8 + 686 z^9) Sin[(7 ArcTan[Sqrt[z]])/4]))/(1675531347 z^(7/2) (1 + z)^(7/8))

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]