Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9cy)

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=1/4

http://functions.wolfram.com/07.23.03.a9cy.01

Input Form

Hypergeometric2F1[-(19/4), 1/4, 4, z] == (1/(140821065 Pi z^3)) (256 (2 Sqrt[1 - z] (3040 - 30685 z + 174420 z^2 + 345682 z^3 - 172204 z^4 + 69795 z^5 - 17696 z^6 + 2048 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (3040 - 32965 z + 197220 z^2 - 883238 z^3 - 47428 z^4 + 18627 z^5 - 4568 z^6 + 512 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (3040 - 30685 z + 174420 z^2 + 345682 z^3 - 172204 z^4 + 69795 z^5 - 17696 z^6 + 2048 z^7) EllipticK[(1/2) (1 - Sqrt[1 - 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]