Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9k8)

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=9/4

http://functions.wolfram.com/07.23.03.a9k8.01

Input Form

Hypergeometric2F1[-(19/4), 9/4, 6, z] == (1/(12814716915 Pi z^5)) (16384 (2 Sqrt[1 - z] (38912 - 238944 z + 535705 z^2 - 368676 z^3 - 430122 z^4 + 1796284 z^5 - 2208423 z^6 + 1403520 z^7 - 468992 z^8 + 65536 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (38912 - 268128 z + 712177 z^2 - 754908 z^3 - 184338 z^4 + 567364 z^5 - 636951 z^6 + 381744 z^7 - 121856 z^8 + 16384 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (38912 - 238944 z + 535705 z^2 - 368676 z^3 - 430122 z^4 + 1796284 z^5 - 2208423 z^6 + 1403520 z^7 - 468992 z^8 + 65536 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]