Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ei)

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=3/4

http://functions.wolfram.com/07.23.03.a9ei.01

Input Form

Hypergeometric2F1[-(19/4), 3/4, 3, z] == (1/(4542615 Pi Sqrt[1 + Sqrt[z]] z^2)) (64 ((-5852 - 5852 Sqrt[z] + 48279 z + 48279 z^(3/2) + 52863 z^2 + 52863 z^(5/2) - 52863 z^3 - 52863 z^(7/2) + 32769 z^4 + 32769 z^(9/2) - 11340 z^5 - 11340 z^(11/2) + 1680 z^6 + 1680 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-2926 + 24871 z - 50376 z^2 + 62970 z^3 - 59874 z^4 + 35415 z^5 - 11760 z^6 + 1680 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))

Standard Form

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MathML Form

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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]