Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9042)

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=-19/4

http://functions.wolfram.com/07.23.03.9042.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), 5, z] == (1/(17876530096425 Pi z^4)) (4096 (2 Sqrt[1 - z] (-26752 + 745712 z - 12480853 z^2 + 217959203 z^3 + 7937315015 z^4 + 27479207567 z^5 + 26706305633 z^6 + 7967641193 z^7 + 579705197 z^8 + 2040885 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-26752 + 745712 z - 12480853 z^2 + 217959203 z^3 + 7937315015 z^4 + 27479207567 z^5 + 26706305633 z^6 + 7967641193 z^7 + 579705197 z^8 + 2040885 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 16 (1672 - 47861 z + 814891 z^2 - 14204267 z^3 + 59629675 z^4 + 1601506123 z^5 + 3880331161 z^6 + 2719601839 z^7 + 583595977 z^8 + 28572390 z^9) 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]