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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, 5/2, -z] == (16 (Sqrt[z] (-3565 + 12844781 z + 145136112 z^2 + 551319296 z^3 + 937345024 z^4 + 737476608 z^5 + 219152384 z^6) Cos[ArcTan[Sqrt[z]]/4] - 2 (-7130 + 374325 z + 8783258 z^2 + 45460096 z^3 + 93282816 z^4 + 83623936 z^5 + 27394048 z^6) Sin[ArcTan[Sqrt[z]]/4]))/ (202504071 z^(3/2) (1 + z)^(1/8))

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]