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

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=35/8, b>=a

For fixed z and a=35/8, b=45/8

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

Input Form

Hypergeometric2F1[35/8, 45/8, -(11/2), -z] == (1/(48345088 (1 + z)^(31/2))) (Sqrt[1 + z] (48345088 + 955090176 z + 9437764640 z^2 + 64017859281 z^3 + 355518292833 z^4 + 1985579043723 z^5 + 20074606218821 z^6 - 99925161105135 z^7 + 88863691075939 z^8 - 20260665427223 z^9 + 849781622679 z^10 + 4135190378 z^11) Cosh[(3 ArcSinh[Sqrt[z]])/4] - 2 Sqrt[z] (18129408 + 360802688 z + 3589740814 z^2 + 24491359125 z^3 + 136520142016 z^4 + 762059446028 z^5 + 21263093188668 z^6 - 68652449160994 z^7 + 51749656304080 z^8 - 10747209707316 z^9 + 425924608934 z^10 + 2067595189 z^11) 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]