Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9176)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-13/4

http://functions.wolfram.com/07.23.03.9176.01

Input Form

Hypergeometric2F1[-(23/4), -(13/4), 5, z] == (1/(157941385977375 Pi z^4)) (4096 Sqrt[1 + Sqrt[z]] (2 (-307648 + 7191272 z - 97779187 z^2 + 1326275335 z^3 + 61825498245 z^4 + 175232800071 z^5 + 120642492831 z^6 + 19003646829 z^7 + 17784975 z^8 - 480675 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (615296 - 615296 Sqrt[z] - 13921072 z + 13921072 z^(3/2) + 185189675 z^2 - 185189675 z^(5/2) - 2515262750 z^3 + 2515262750 z^(7/2) - 48396522195 z^4 + 48396522195 z^(9/2) - 93994609632 z^5 + 93994609632 z^(11/2) - 41403741771 z^6 + 41403741771 z^(13/2) - 2908083750 z^7 + 2908083750 z^(15/2) + 69697875 z^8 - 69697875 z^(17/2) - 1922700 z^9 + 1922700 z^(19/2)) 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]