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

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=-11/4, b>=a

For fixed z and a=-11/4, b=13/4

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

Input Form

Hypergeometric2F1[-(11/4), 13/4, 11/2, z] == (1/(2403375 Pi^(3/2) z^(9/2))) (32 (-2 (-25872 + 63756 z - 14245 z^2 - 17710 z^3 - 69685 z^4 + 196876 z^5 - 155648 z^6 + 40960 z^7) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (-25872 + 63756 z - 14245 z^2 - 17710 z^3 - 69685 z^4 + 196876 z^5 - 155648 z^6 + 40960 z^7) EllipticE[(1/2) (1 + Sqrt[z])] + (-25872 - 12936 Sqrt[z] + 63756 z + 30800 z^(3/2) - 14245 z^2 - 5005 z^(5/2) - 17710 z^3 - 8470 z^(7/2) - 69685 z^4 + 39835 z^(9/2) + 196876 z^5 - 36032 z^(11/2) - 155648 z^6 + 10240 z^(13/2) + 40960 z^7) EllipticK[(1/2) (1 - Sqrt[z])] - (-25872 + 12936 Sqrt[z] + 63756 z - 30800 z^(3/2) - 14245 z^2 + 5005 z^(5/2) - 17710 z^3 + 8470 z^(7/2) - 69685 z^4 - 39835 z^(9/2) + 196876 z^5 + 36032 z^(11/2) - 155648 z^6 - 10240 z^(13/2) + 40960 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

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]