Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8vd)

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=-21/4, b>=a

For fixed z and a=-21/4, b=19/4

http://functions.wolfram.com/07.23.03.a8vd.01

Input Form

Hypergeometric2F1[-(21/4), 19/4, 2, z] == -((1/(19144125 Pi z)) (8 (2 (51051 - 8986139 z + 89894500 z^2 - 312217600 z^3 + 491315200 z^4 - 360710144 z^5 + 100663296 z^6) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (-51051 (1 + Sqrt[1 - z]) + (8986139 + 4187345 Sqrt[1 - z]) z - 100 (898945 + 300752 Sqrt[1 - z]) z^2 + 51200 (6098 + 1423 Sqrt[1 - z]) z^3 - 204800 (2399 + 352 Sqrt[1 - z]) z^4 + 8388608 (43 + 3 Sqrt[1 - z]) z^5 - 100663296 z^6) 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]