Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8030)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=4/3, b>=a

For fixed z and a=4/3, b=17/3

http://functions.wolfram.com/07.23.03.8030.01

Input Form

Hypergeometric2F1[4/3, 17/3, -(11/2), z] == ((1/Sqrt[1 - z]) ((443418624 - 6176507904 z + 40871596032 z^2 - 173197963264 z^3 + 544318035968 z^4 - 1476807563264 z^5 + 5535860228096 z^6 + 8198334275867 z^7 - 224125948304 z^8 + 36779089688 z^9 - 4626674848 z^10 + 297535360 z^11) Cos[ArcSin[Sqrt[z]]/3]) + Sqrt[z] (147806208 - 1954824192 z + 12259602432 z^2 - 49250164736 z^3 + 147653896192 z^4 - 391732273152 z^5 - 3697465746257 z^6 - 207378426728 z^7 + 34577328024 z^8 - 4477907168 z^9 + 297535360 z^10) Sin[ArcSin[Sqrt[z]]/3])/(443418624 (-1 + z)^12)

Standard Form

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MathML Form

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<ci> cos </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 3 </cn> <apply> <times /> <apply> <power /> <ci> sin </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 297535360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4477907168 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 34577328024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 207378426728 </cn> <apply> <power /> <ci> z </ci> <cn 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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]