Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.1098)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a=-11/2, b>=a

For fixed z and a=-11/2, b=11/2

http://functions.wolfram.com/07.23.03.1098.01

Input Form

Hypergeometric2F1[-(11/2), 11/2, 4, z] == (1/(3828825 Pi z^3)) ( -32 (88 + z (957 + z (12518 + z (-654595 + 8 z (467595 + 16 z (-68377 + 128 z (619 - 354 z + 80 z^2))))))) EllipticE[z] + 32 (-1 + z) (-88 + z (-1001 + z (-13035 + 4 z (102145 + 16 z (-27955 + 32 z (1497 + 16 z (-71 + 20 z))))))) EllipticK[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]