Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9jx)

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=-19/4, b>=a

For fixed z and a=-19/4, b=9/4

http://functions.wolfram.com/07.23.03.a9jx.01

Input Form

Hypergeometric2F1[-(19/4), 9/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-5852 + 13167 z + 206478 z^2 + 524339 z^3 + 586368 z^4 + 313344 z^5 + 65536 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-5852 + 7315 z + 219645 z^2 + 730817 z^3 + 1110707 z^4 + 899712 z^5 + 378880 z^6 + 65536 z^7) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 2 (-2926 + 4389 z + 37404 z^2 + 81745 z^3 + 83256 z^4 + 41472 z^5 + 8192 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (-5852 + 13167 z + 206478 z^2 + 524339 z^3 + 586368 z^4 + 313344 z^5 + 65536 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (4542615 Pi z^2 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </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]