Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9666)

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=7/4

http://functions.wolfram.com/07.23.03.9666.01

Input Form

Hypergeometric2F1[-(23/4), 7/4, 5, z] == (4096 ((-(-615296 - 615296 Sqrt[z] + 4383984 z + 4383984 z^(3/2) - 11522379 z^2 - 11522379 z^(5/2) + 6056820 z^3 + 6056820 z^(7/2) - 21304530 z^4 - 21304530 z^(9/2) + 30022668 z^5 + 30022668 z^(11/2) - 24607947 z^6 - 24607947 z^(13/2) + 12183912 z^7 + 12183912 z^(15/2) - 3397680 z^8 - 3397680 z^(17/2) + 411840 z^9 + 411840 z^(19/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + 8 (-76912 + 567226 z - 1571889 z^2 + 1081575 z^3 + 2258100 z^4 - 6654024 z^5 + 8745087 z^6 - 6823713 z^7 + 3246750 z^8 - 875160 z^9 + 102960 z^10) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (82380323025 Pi Sqrt[1 + Sqrt[z]] z^4)

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]