Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8761)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=13/3, b>=a

For fixed z and a=13/3, b=14/3

http://functions.wolfram.com/07.23.03.8761.01

Input Form

Hypergeometric2F1[13/3, 14/3, -(9/2), -z] == (3 (71663616 + 1293484032 z + 11854970880 z^2 + 77581385728 z^3 + 465413701632 z^4 + 4632613945344 z^5 - 27073741329895 z^6 + 25177001676936 z^7 - 5650136403936 z^8 + 224819720512 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (71663616 + 1243054080 z + 10985734144 z^2 + 69943492608 z^3 + 416993280000 z^4 - 20742211552543 z^5 + 31006744022832 z^6 - 9727800858624 z^7 + 526227045184 z^8) Sinh[ArcSinh[Sqrt[z]]/3])/ (214990848 (1 + z)^(27/2))

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]