Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9er)

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=-19/4, b>=a

For fixed z and a=-19/4, b=3/4

http://functions.wolfram.com/07.23.03.a9er.01

Input Form

Hypergeometric2F1[-(19/4), 3/4, 5, -z] == (1/(27460107675 Pi z^4)) (4096 (1 + z)^(1/4) (2 (-80256 - 745712 z - 3182025 z^2 - 8778000 z^3 + 3678090 z^4 + 2316132 z^5 + 985959 z^6 + 248820 z^7 + 28080 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 2 Sqrt[1 + z] (40128 + 342760 z + 1338645 z^2 + 3423420 z^3 + 2440230 z^4 + 1718964 z^5 + 817245 z^6 + 227760 z^7 + 28080 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-80256 - 745712 z - 3182025 z^2 - 8778000 z^3 + 3678090 z^4 + 2316132 z^5 + 985959 z^6 + 248820 z^7 + 28080 z^8) EllipticK[1/2 - 1/(2 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]