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

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=37/8

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

Input Form

Hypergeometric2F1[27/8, 37/8, -(9/2), -z] == (1/(29696 (1 + z)^(25/2))) (-2 Sqrt[1 + z] (-14848 - 233856 z - 1842486 z^2 - 10180827 z^3 - 50505936 z^4 - 407383677 z^5 + 1379544946 z^6 - 666689909 z^7 + 48657972 z^8 + 368621 z^9) Cosh[(3 ArcSinh[Sqrt[z]])/4] + Sqrt[z] (-22272 - 354032 z - 2812855 z^2 - 15643760 z^3 - 77755757 z^4 - 1567926518 z^5 + 3506953007 z^6 - 1452657700 z^7 + 97684565 z^8 + 737242 z^9) Sinh[(3 ArcSinh[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]