Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bam6)

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=37/8

http://functions.wolfram.com/07.23.03.bam6.01

Input Form

Hypergeometric2F1[-(39/8), 37/8, -(11/2), -z] == (1/(9146368 (1 + z)^(41/8))) ((-(-9146368 - 9094400 z + 4774560 z^2 - 5236617 z^3 + 8471190 z^4 - 21828677 z^5 + 152843340 z^6 + 963663360 z^7 + 1548045312 z^8 + 1020067840 z^9 + 245104640 z^10)) Cos[ArcTan[Sqrt[z]]/4] + Sqrt[z] (2286592 + 1559040 z - 1493268 z^2 + 1806555 z^3 - 2808650 z^4 + 6544343 z^5 + 158183520 z^6 + 318329088 z^7 + 235868160 z^8 + 61276160 z^9) Sin[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]