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

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=-15/8, b>=a

For fixed z and a=-15/8, b=-3/8

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

Input Form

Hypergeometric2F1[-(15/8), -(3/8), 11/2, -z] == -((1024 (4 Sqrt[z] (-560 - 4850 z - 19689 z^2 - 53886 z^3 - 1209716 z^4 + 222456 z^5 + 9269 z^6) Cos[ArcTan[Sqrt[z]]/4] + (8960 + 80400 z + 338539 z^2 + 954636 z^3 + 3007074 z^4 - 3227396 z^5 - 9269 z^6) Sin[ArcTan[Sqrt[z]]/4]))/(4248325653 z^(9/2) (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]