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

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=19/4

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

Input Form

Hypergeometric2F1[-(13/4), 19/4, 5, -z] == (4096 Sqrt[2] (4 (-1248 + 2340 z - 6357 z^2 + 30225 z^3 + 710000 z^4 + 1724288 z^5 + 1515520 z^6 + 458752 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 4 Sqrt[1 + z] (-1248 + 2340 z - 6357 z^2 + 30225 z^3 + 710000 z^4 + 1724288 z^5 + 1515520 z^6 + 458752 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-4992 + 10608 z - 28665 z^2 + 129675 z^3 + 905600 z^4 + 1185792 z^5 + 458752 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 4 (-1248 + 2340 z - 6357 z^2 + 30225 z^3 + 710000 z^4 + 1724288 z^5 + 1515520 z^6 + 458752 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (3886257375 Pi z^4 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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</semantics> </math>

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]