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

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.barj.01

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(11/2), -z] == (1/(338415616 (1 + z)^(49/8))) ((-(-338415616 - 374949120 z + 215115040 z^2 - 260645649 z^3 + 477973215 z^4 - 1440806159 z^5 + 12199307185 z^6 + 96187615920 z^7 + 206144742144 z^8 + 203834245120 z^9 + 97980579840 z^10 + 18627952640 z^11)) Cos[ArcTan[Sqrt[z]]/4] + 2 Sqrt[z] (42301952 + 33649280 z - 33934698 z^2 + 44148585 z^3 - 76601470 z^4 + 209193153 z^5 + 7246475170 z^6 + 19717196928 z^7 + 22070315520 z^8 + 11519918080 z^9 + 2328494080 z^10) 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]