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

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=-3/4

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

Input Form

Hypergeometric2F1[-(17/4), -(3/4), 4, z] == -((1/(3886257375 Pi z^3)) (256 Sqrt[1 + Sqrt[z]] ((-21216 + 284427 z - 2426580 z^2 - 40570070 z^3 - 17948700 z^4 + 2272347 z^5 - 338184 z^6 + 27720 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (21216 - 21216 Sqrt[z] - 268515 z + 268515 z^(3/2) + 2227680 z^2 - 2227680 z^(5/2) + 11848910 z^3 - 11848910 z^(7/2) + 993300 z^4 - 993300 z^(9/2) - 156387 z^5 + 156387 z^(11/2) + 13860 z^6 - 13860 z^(13/2)) 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]