Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ae8y)

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=-9/4, b>=a

For fixed z and a=-9/4, b=3/4

http://functions.wolfram.com/07.23.03.ae8y.01

Input Form

Hypergeometric2F1[-(9/4), 3/4, 6, z] == (1/(2230812675 Pi z^5)) (16384 (2 (6144 - 46944 z + 157417 z^2 - 306500 z^3 + 402550 z^4 + 221884 z^5 - 57239 z^6 + 7072 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-6144 + 45408 z - 146785 z^2 + 274675 z^3 - 348075 z^4 - 13039 z^5 + 1768 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (6144 - 46944 z + 157417 z^2 - 306500 z^3 + 402550 z^4 + 221884 z^5 - 57239 z^6 + 7072 z^7) 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]