Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bn37)

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=-19/8, b>=a

For fixed z and a=-19/8, b=41/8

http://functions.wolfram.com/07.23.03.bn37.01

Input Form

Hypergeometric2F1[-(19/8), 41/8, 9/2, -z] == -((256 (Sqrt[z] (-7600 + 28785 z - 122835 z^2 - 146608 z^3 + 4427136 z^4 + 8902656 z^5 + 4472832 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - (-6080 + 24168 z - 102771 z^2 + 943369 z^3 + 7646688 z^4 + 12176640 z^5 + 5591040 z^6) Sin[(5 ArcTan[Sqrt[z]])/4]))/ (333266895 z^(7/2) (1 + z)^(5/8)))

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]