Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aay9)

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=21/4

http://functions.wolfram.com/07.23.03.aay9.01

Input Form

Hypergeometric2F1[-(17/4), 21/4, 6, z] == (16384 ((-2048 - 2048 Sqrt[z] - 1568 z - 1568 z^(3/2) - 2467 z^2 - 2467 z^(5/2) - 6180 z^3 - 6180 z^(7/2) - 29535 z^4 - 29535 z^(9/2) + 1158806 z^5 + 1158806 z^(11/2) - 3630704 z^6 - 3630704 z^(13/2) + 4585504 z^7 + 4585504 z^(15/2) - 2661120 z^8 - 2661120 z^(17/2) + 591360 z^9 + 591360 z^(19/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (-2048 - 1056 z - 1931 z^2 - 5375 z^3 - 27705 z^4 + 665291 z^5 - 1958968 z^6 + 2391312 z^7 - 1355200 z^8 + 295680 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/(4108329225 Pi Sqrt[1 + Sqrt[z]] z^5)

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]