Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9216)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-11/4

http://functions.wolfram.com/07.23.03.9216.01

Input Form

Hypergeometric2F1[-(23/4), -(11/4), 6, z] == (1/(65887782355395 Pi z^5)) (16384 (2 Sqrt[1 - z] (22528 - 456544 z + 4892481 z^2 - 40456229 z^3 + 374960201 z^4 + 6046869051 z^5 + 9048919771 z^6 + 2830134761 z^7 + 68619771 z^8 - 2979999 z^9 + 98208 z^10) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (22528 - 473440 z + 5233305 z^2 - 44094215 z^3 + 404972645 z^4 - 2274597795 z^5 - 16205201885 z^6 - 15488783125 z^7 - 3057598665 z^8 - 751905 z^9 + 24552 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (22528 - 456544 z + 4892481 z^2 - 40456229 z^3 + 374960201 z^4 + 6046869051 z^5 + 9048919771 z^6 + 2830134761 z^7 + 68619771 z^8 - 2979999 z^9 + 98208 z^10) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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<times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 456544 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 22528 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]