Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a94v)

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=-11/4

http://functions.wolfram.com/07.23.03.a94v.01

Input Form

Hypergeometric2F1[-(19/4), -(11/4), -(1/2), z] == (1/(390 Pi^(3/2))) ((2 Sqrt[z] (195 + 79467 z + 112557 z^2 + 4697 z^3 - 308 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-195 - 79467 z - 112557 z^2 - 4697 z^3 + 308 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (390 - 195 Sqrt[z] - 10335 z - 79467 z^(3/2) - 105351 z^2 - 112557 z^(5/2) - 81389 z^3 - 4697 z^(7/2) + 77 z^4 + 308 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (390 + 195 Sqrt[z] - 10335 z + 79467 z^(3/2) - 105351 z^2 + 112557 z^(5/2) - 81389 z^3 + 4697 z^(7/2) + 77 z^4 - 308 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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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]