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

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=-13/4, b>=a

For fixed z and a=-13/4, b=15/4

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

Input Form

Hypergeometric2F1[-(13/4), 15/4, 5, z] == (1/(777251475 Pi z^4)) (4096 (-2 (-14976 + 8112 z + 10803 z^2 + 33150 z^3 - 542065 z^4 + 1042304 z^5 - 759808 z^6 + 196608 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 Sqrt[1 - z] (3744 - 1092 z - 2535 z^2 - 8775 z^3 + 38260 z^4 - 38656 z^5 + 12288 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-14976 + 8112 z + 10803 z^2 + 33150 z^3 - 542065 z^4 + 1042304 z^5 - 759808 z^6 + 196608 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]