Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b71y)

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=31/8

http://functions.wolfram.com/07.23.03.b71y.01

Input Form

Hypergeometric2F1[-(45/8), 31/8, 11/2, -z] == (1024 (4 Sqrt[z] (-360528 - 633070 z + 473193 z^2 - 1139526 z^3 + 28250816 z^4 + 153275052 z^5 + 325058175 z^6 + 368934720 z^7 + 238461696 z^8 + 83263488 z^9 + 12255232 z^10) Cos[(3 ArcTan[Sqrt[z]])/4] - (-1922816 - 3656784 z + 2095569 z^2 - 5626812 z^3 + 49347270 z^4 + 361671348 z^5 + 846401969 z^6 + 1015087392 z^7 + 680967936 z^8 + 244428800 z^9 + 36765696 z^10) Sin[(3 ArcTan[Sqrt[z]])/4]))/(77044264605 z^(9/2) (1 + z)^(3/8))

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]