Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ag5m)

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=-5/4, b>=a

For fixed z and a=-5/4, b=13/4

http://functions.wolfram.com/07.23.03.ag5m.01

Input Form

Hypergeometric2F1[-(5/4), 13/4, 6, z] == (1/(21928725 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((-(2048 + 2048 Sqrt[z] - 5216 z - 5216 z^(3/2) + 2835 z^2 + 2835 z^(5/2) + 910 z^3 + 910 z^(7/2) + 875 z^4 + 875 z^(9/2) - 4956 z^5 - 4956 z^(11/2) + 2352 z^6 + 2352 z^(13/2))) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (2048 - 5728 z + 3995 z^2 + 490 z^3 + 595 z^4 - 2576 z^5 + 1176 z^6) 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]