Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6sh)

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=17/8, b>=a

For fixed z and a=17/8, b=47/8

http://functions.wolfram.com/07.23.03.c6sh.01

Input Form

Hypergeometric2F1[17/8, 47/8, -(11/2), -z] == (1/(289124352 (1 + z)^(27/2))) (Sqrt[1 + z] (289124352 + 4423931136 z + 32784972064 z^2 + 160069076817 z^3 + 606331171550 z^4 + 2149160865319 z^5 + 12530956379292 z^6 - 21151918497609 z^7 + 2453997780654 z^8 + 204341975145 z^9 + 18066598872 z^10 + 915818376 z^11) Cosh[ArcSinh[Sqrt[z]]/4] - 4 Sqrt[z] (18070272 + 282142656 z + 2133065701 z^2 + 10609325207 z^3 + 40770363868 z^4 + 144981128383 z^5 + 18911808000576 z^6 - 14886997059825 z^7 + 638491920504 z^8 + 53315199321 z^9 + 4631127015 z^10 + 228954594 z^11) Sinh[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]