Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aa7m)

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=-17/4, b>=a

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

http://functions.wolfram.com/07.23.03.aa7m.01

Input Form

Hypergeometric2F1[-(17/4), -(17/4), 6, z] == (1/(5091514033480875 Pi z^5)) (16384 ((2715648 - 57919680 z + 655387434 z^2 - 5732888070 z^3 + 56028463218 z^4 + 2890838930658 z^5 + 7225967474110 z^6 + 4632301742574 z^7 + 804247965990 z^8 + 25251001718 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (1357824 (1 + Sqrt[1 - z]) - 21216 (1365 + 1349 Sqrt[1 - z]) z + 663 (494259 + 483707 Sqrt[1 - z]) z^2 - 4641 (617635 + 601061 Sqrt[1 - z]) z^3 + 4641 (6036249 + 5893645 Sqrt[1 - z]) z^4 + 21 (68829498349 + 39544286679 Sqrt[1 - z]) z^5 + 7 (516140533865 + 262289998073 Sqrt[1 - z]) z^6 + (2316150871287 + 1051801353401 Sqrt[1 - z]) z^7 + (402123982995 + 160149711479 Sqrt[1 - z]) z^8 + (12625500859 + 4108329225 Sqrt[1 - z]) z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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<ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1365 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1357824 </cn> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> </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]