Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6sk)

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.c6sk.01

Input Form

Hypergeometric2F1[17/8, 47/8, -(9/2), z] == (1/(45997056 (1 - z)^(25/2))) (4 Sqrt[1 - z] (11499264 - 170252992 z + 1244887305 z^2 - 6271535879 z^3 + 27660139825 z^4 - 191592401085 z^5 - 383441372127 z^6 - 51628237305 z^7 + 4812652863 z^8 - 471728355 z^9 + 26273478 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (11499264 - 173846512 z + 1296564119 z^2 - 6638841394 z^3 + 29467235473 z^4 - 4944672267012 z^5 - 4478849149887 z^6 - 215908959138 z^7 + 20180931423 z^8 - 1939460376 z^9 + 105093912 z^10) Sin[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]