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

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=27/8, b>=a

For fixed z and a=27/8, b=47/8

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

Input Form

Hypergeometric2F1[27/8, 47/8, -(11/2), -z] == (1/(45056 (1 + z)^(115/8))) ((45056 + 797440 z + 6990368 z^2 + 41601455 z^3 + 200340811 z^4 + 960702743 z^5 + 8344867531 z^6 - 25643015419 z^7 + 12409271161 z^8 - 858980507 z^9 - 21326767 z^10 - 587312 z^11) Cos[(3 ArcTan[Sqrt[z]])/4] + 2 Sqrt[z] (16896 + 296576 z + 2578702 z^2 + 15234131 z^3 + 72987838 z^4 + 350090741 z^5 - 9742454708 z^6 + 10942887725 z^7 - 2236709258 z^8 + 7965419 z^9 + 220242 z^10) 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]