Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a922)

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=-17/4

http://functions.wolfram.com/07.23.03.a922.01

Input Form

Hypergeometric2F1[-(19/4), -(17/4), 6, z] == (1/(3506298768697725 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((661504 - 14790816 z + 176715561 z^2 - 1648257695 z^3 + 17425493085 z^4 + 671902782117 z^5 + 1729718666907 z^6 + 1188973865763 z^7 + 232542132255 z^8 + 9213428535 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-661504 + 661504 Sqrt[z] + 14294688 z - 14294688 z^(3/2) - 166072065 z^2 + 166072065 z^(5/2) + 1525349735 z^3 - 1525349735 z^(7/2) - 16300329045 z^4 + 16300329045 z^(9/2) - 255941276157 z^5 + 255941276157 z^(11/2) - 456678307491 z^6 + 456678307491 z^(13/2) - 210560824395 z^7 + 210560824395 z^(15/2) - 23662503495 z^8 + 23662503495 z^(17/2) - 302344575 z^9 + 302344575 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]