Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9043)

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/07.23.03.9043.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), 5, -z] == (4096 Sqrt[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 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (26752 + 772464 z + 13226565 z^2 + 230440056 z^3 - 7719355812 z^4 + 19541892552 z^5 + 772901934 z^6 - 18738664440 z^7 + 7387935996 z^8 - 577664312 z^9 + 2040885 z^10) EllipticE[(-1 + Sqrt[1 + z])/ (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 + Sqrt[1 + z])/(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 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (17876530096425 Pi z^4 Sqrt[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]