Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.1460)

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=-9/2, b>=a

For fixed z and a=-9/2, b=9/2

http://functions.wolfram.com/07.23.03.1460.01

Input Form

Hypergeometric2F1[-(9/2), 9/2, 5, z] == (1/(3828825 Pi z^4)) (256 ((-144 + z (-240 + z (-645 + z (-3294 + z (71555 + 32 z (-6581 + 4 z (2025 + 8 z (-145 + 32 z)))))))) EllipticE[z] - 4 (-1 + z) (36 + z (78 + z (207 + z (945 + 2 z (-4945 + 16 z (609 + 4 z (-117 + 32 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]