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

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=-3/4, b>=a

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

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

Input Form

Hypergeometric2F1[-(3/4), 17/4, 11/2, z] == (1/(43095 Pi^(3/2) z^(9/2))) (32 (-2 (1680 - 420 z - 371 z^2 - 525 z^3 - 1632 z^4 + 2048 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (1680 - 420 z - 371 z^2 - 525 z^3 - 1632 z^4 + 2048 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (1680 + 840 Sqrt[z] - 420 z - 140 z^(3/2) - 371 z^2 - 168 z^(5/2) - 525 z^3 - 264 z^(7/2) - 1632 z^4 + 512 z^(9/2) + 2048 z^5) EllipticK[(1/2) (1 - Sqrt[z])] - (1680 - 840 Sqrt[z] - 420 z + 140 z^(3/2) - 371 z^2 + 168 z^(5/2) - 525 z^3 + 264 z^(7/2) - 1632 z^4 - 512 z^(9/2) + 2048 z^5) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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<cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </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]