Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aat0)

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=-17/4, b>=a

For fixed z and a=-17/4, b=15/4

http://functions.wolfram.com/07.23.03.aat0.01

Input Form

Hypergeometric2F1[-(17/4), 15/4, 6, z] == (1/(316341350325 Pi z^5)) (16384 (2 (-1357824 + 3840096 z - 1137045 z^2 - 1229865 z^3 - 3411135 z^4 + 55496861 z^5 - 119142464 z^6 + 112135680 z^7 - 50954240 z^8 + 9175040 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (1357824 - 3500640 z + 421005 z^2 + 1024335 z^3 + 3530475 z^4 - 15975431 z^5 + 20231040 z^6 - 11089920 z^7 + 2293760 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-1357824 + 3840096 z - 1137045 z^2 - 1229865 z^3 - 3411135 z^4 + 55496861 z^5 - 119142464 z^6 + 112135680 z^7 - 50954240 z^8 + 9175040 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]