Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ia)

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=-19/4, b>=a

For fixed z and a=-19/4, b=7/4

http://functions.wolfram.com/07.23.03.a9ia.01

Input Form

Hypergeometric2F1[-(19/4), 7/4, 5, z] == (4096 (2 (13376 + 13376 Sqrt[z] - 85272 z - 85272 z^(3/2) + 197505 z^2 + 197505 z^(5/2) - 87780 z^3 - 87780 z^(7/2) + 251190 z^4 + 251190 z^(9/2) - 281628 z^5 - 281628 z^(11/2) + 172641 z^6 + 172641 z^(13/2) - 56880 z^7 - 56880 z^(15/2) + 7920 z^8 + 7920 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (26752 - 177232 z + 435765 z^2 - 263340 z^3 - 507090 z^4 + 1220364 z^5 - 1275339 z^6 + 743880 z^7 - 235440 z^8 + 31680 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(2112315975 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]