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

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=-5/4, b>=a

For fixed z and a=-5/4, b=1/4

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

Input Form

Hypergeometric2F1[-(5/4), 1/4, 6, z] == -((1/(1527701175 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((-2048 + 14816 z - 47235 z^2 + 89215 z^3 - 124075 z^4 - 136059 z^5 + 8778 z^6) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (2048 - 2048 Sqrt[z] - 13280 z + 13280 z^(3/2) + 37515 z^2 - 37515 z^(5/2) - 62545 z^3 + 62545 z^(7/2) + 81025 z^4 - 81025 z^(9/2) + 4389 z^5 - 4389 z^(11/2)) 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]