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

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=19/4

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

Input Form

Hypergeometric2F1[19/4, 19/4, 5, z] == (1/(1334025 Pi (-1 + z)^5 z^4)) (4096 (8 (-1 + z) (-32 + 132 z - 213 z^2 + 183 z^3) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 (-1 + z) (-32 + 132 z - 213 z^2 + 183 z^3) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (128 - 624 z + 1239 z^2 - 1338 z^3 + 1155 z^4) 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]