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

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=-37/8, b>=a

For fixed z and a=-37/8, b=15/8

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

Input Form

Hypergeometric2F1[-(37/8), 15/8, 5/2, -z] == (1/(5635245 z^(3/2) (1 + z)^(3/8))) (16 (Sqrt[z] (-41847 + 546617 z + 2598567 z^2 + 4808439 z^3 + 4498208 z^4 + 2126592 z^5 + 405504 z^6) Cos[(3 ArcTan[Sqrt[z]])/4] - 2 (-27898 + 125541 z + 783654 z^2 + 1596437 z^3 + 1578846 z^4 + 775296 z^5 + 152064 z^6) Sin[(3 ArcTan[Sqrt[z]])/4]))

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]