Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ac8n)

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=-9/4

http://functions.wolfram.com/07.23.03.ac8n.01

Input Form

Hypergeometric2F1[-(13/4), -(9/4), 5, z] == (1/(30030170625 Pi z^4)) (4096 (2 (-1152 + 17328 z - 141675 z^2 + 1053075 z^3 + 32004050 z^4 + 36893558 z^5 + 6551753 z^6 + 26775 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 2 Sqrt[1 - z] (-576 + 8520 z - 68775 z^2 + 510300 z^3 + 8790550 z^4 + 8602484 z^5 + 1258425 z^6) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (-1152 + 17328 z - 141675 z^2 + 1053075 z^3 + 32004050 z^4 + 36893558 z^5 + 6551753 z^6 + 26775 z^7) EllipticK[(1/2) (1 - Sqrt[1 - 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]