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

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=33/8, b>=a

For fixed z and a=33/8, b=47/8

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

Input Form

Hypergeometric2F1[33/8, 47/8, -(5/2), -z] == (1/(1140800 (1 + z)^(25/2))) (2 Sqrt[1 + z] (570400 + 12391940 z + 169319675 z^2 + 3363114050 z^3 - 26199102463 z^4 + 32314568064 z^5 - 8621726931 z^6 + 230319450 z^7 + 4265175 z^8) Cosh[ArcSinh[Sqrt[z]]/4] - Sqrt[z] (285200 + 6285095 z + 86558200 z^2 + 72733594221 z^3 - 255258315122 z^4 + 200157295233 z^5 - 36011521188 z^6 + 464904075 z^7 + 8530350 z^8) 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]