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

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=-13/4, b>=a

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

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

Input Form

Hypergeometric2F1[-(13/4), 11/4, 11/2, z] == (1/(9388071 Pi^(3/2) z^(9/2))) (8 (-8 Sqrt[z] (1950 - 6825 z + 5265 z^2 + 3900 z^3 - 64413 z^4 + 89307 z^5 - 49664 z^6 + 10240 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 8 Sqrt[z] (1950 - 6825 z + 5265 z^2 + 3900 z^3 - 64413 z^4 + 89307 z^5 - 49664 z^6 + 10240 z^7) EllipticE[(1/2) (1 + Sqrt[z])] + (-15600 + 7800 Sqrt[z] + 66300 z - 27300 z^(3/2) - 81315 z^2 + 21060 z^(5/2) - 4875 z^3 + 15600 z^(7/2) - 45825 z^4 - 257652 z^(9/2) + 76899 z^5 + 357228 z^(11/2) - 46784 z^6 - 198656 z^(13/2) + 10240 z^7 + 40960 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (15600 + 7800 Sqrt[z] - 66300 z - 27300 z^(3/2) + 81315 z^2 + 21060 z^(5/2) + 4875 z^3 + 15600 z^(7/2) + 45825 z^4 - 257652 z^(9/2) - 76899 z^5 + 357228 z^(11/2) + 46784 z^6 - 198656 z^(13/2) - 10240 z^7 + 40960 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^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]