Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9256)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-9/4

http://functions.wolfram.com/07.23.03.9256.01

Input Form

Hypergeometric2F1[-(23/4), -(9/4), 3, z] == (1/(31121455365 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] ((-672980 + 22040095 z + 1624335477 z^2 + 5094984834 z^3 + 2643441654 z^4 + 12202515 z^5 - 1156935 z^6 + 66300 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 4 (-168245 + 168245 Sqrt[z] + 5383840 z - 5383840 z^(3/2) + 166965663 z^2 - 166965663 z^(5/2) + 335872362 z^3 - 335872362 z^(7/2) + 84317025 z^4 - 84317025 z^(9/2) - 5688540 z^5 + 5688540 z^(11/2) + 553605 z^6 - 553605 z^(13/2) - 33150 z^7 + 33150 z^(15/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]