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

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=37/8

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

Input Form

Hypergeometric2F1[35/8, 37/8, -(9/2), z] == -((1/(801792 (1 - z)^(27/2))) (Sqrt[1 - z] (-801792 + 14254080 z - 128861268 z^2 + 834702273 z^3 - 4996494738 z^4 + 50618706183 z^5 + 235263774720 z^6 + 179132271647 z^7 + 30547661638 z^8 + 706646457 z^9) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (-601344 + 10778256 z - 98150181 z^2 + 639185607 z^3 - 3830522913 z^4 + 105698482091 z^5 + 316686188961 z^6 + 204304363269 z^7 + 31872775397 z^8 + 706646457 z^9) Sin[(3 ArcSin[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]