Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a8ub)

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=17/4

http://functions.wolfram.com/07.23.03.a8ub.01

Input Form

Hypergeometric2F1[-(21/4), 17/4, 6, z] == -((1/(168441498225 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((-243712 + 422688 z + 243355 z^2 + 374969 z^3 + 1361955 z^4 - 47235661 z^5 + 149787814 z^6 - 212205840 z^7 + 159502112 z^8 - 62388480 z^9 + 10053120 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (243712 - 243712 Sqrt[z] - 239904 z + 239904 z^(3/2) - 394723 z^2 + 394723 z^(5/2) - 688415 z^3 + 688415 z^(7/2) - 1929585 z^4 + 1929585 z^(9/2) + 25126651 z^5 - 25126651 z^(11/2) - 56030392 z^6 + 56030392 z^(13/2) + 55554576 z^7 - 55554576 z^(15/2) - 26586560 z^8 + 26586560 z^(17/2) + 5026560 z^9 - 5026560 z^(19/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]