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

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=1/4, b>=a

For fixed z and a=1/4, b=15/4

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

Input Form

Hypergeometric2F1[1/4, 15/4, 6, z] == -((1/(1689765 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((2048 - 2656 z + 115 z^2 + 85 z^3 + 100 z^4) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-2048 + 2048 Sqrt[z] + 1120 z - 1120 z^(3/2) + 485 z^2 - 485 z^(5/2) + 320 z^3 - 320 z^(7/2) + 200 z^4 - 200 z^(9/2)) 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]