Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8xn)

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=-21/4, b>=a

For fixed z and a=-21/4, b=21/4

http://functions.wolfram.com/07.23.03.a8xn.01

Input Form

Hypergeometric2F1[-(21/4), 21/4, 6, z] == (16384 ((-(43008 + 43008 Sqrt[z] + 35616 z + 35616 z^(3/2) + 62671 z^2 + 62671 z^(5/2) + 180075 z^3 + 180075 z^(7/2) + 1008105 z^4 + 1008105 z^(9/2) - 48536191 z^5 - 48536191 z^(11/2) + 190547148 z^6 + 190547148 z^(13/2) - 321282192 z^7 - 321282192 z^(15/2) + 279910400 z^8 + 279910400 z^(17/2) - 124481280 z^9 - 124481280 z^(19/2) + 22471680 z^10 + 22471680 z^(21/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (43008 + 24864 z + 50743 z^2 + 160265 z^3 + 956235 z^4 - 28243261 z^5 + 104289922 z^6 - 170014416 z^7 + 144673760 z^8 - 63176960 z^9 + 11235840 z^10) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (168441498225 Pi Sqrt[1 + Sqrt[z]] z^5)

Standard Form

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MathML Form

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</apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 168441498225 </cn> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]