Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8z2)

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=-21/4, b>=a

For fixed z and a=-21/4, b=23/4

http://functions.wolfram.com/07.23.03.a8z2.01

Input Form

Hypergeometric2F1[-(21/4), 23/4, 5, z] == (1/(4293204040125 Pi z^4)) (4096 (-2 (254592 + 1389648 z + 7883733 z^2 + 71135922 z^3 - 3475304935 z^4 + 17141637152 z^5 - 35436439552 z^6 + 36965449728 z^7 - 19302187008 z^8 + 4026531840 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 Sqrt[1 - z] (-63648 - 363324 z - 2069223 z^2 - 18348525 z^3 + 339893950 z^4 - 1136933248 z^5 + 1591689216 z^6 - 1025507328 z^7 + 251658240 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (254592 + 1389648 z + 7883733 z^2 + 71135922 z^3 - 3475304935 z^4 + 17141637152 z^5 - 35436439552 z^6 + 36965449728 z^7 - 19302187008 z^8 + 4026531840 z^9) 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]