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

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=-19/8, b>=a

For fixed z and a=-19/8, b=-7/8

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

Input Form

Hypergeometric2F1[-(19/8), -(7/8), 9/2, -z] == (1/(11762361 z^(7/2) (1 + z)^(5/8))) (256 (Sqrt[z] (80 + 825 z + 4536 z^2 + 73758 z^3 - 82268 z^4 + 6993 z^5 + 252 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - (64 + 648 z + 3507 z^2 + 21588 z^3 - 104598 z^4 + 36028 z^5 + 315 z^6) Sin[(5 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]