Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a99k)

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=-5/4

http://functions.wolfram.com/07.23.03.a99k.01

Input Form

Hypergeometric2F1[-(19/4), -(5/4), 6, z] == (1/(127442359719675 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((428032 - 6440544 z + 48746115 z^2 - 265344310 z^3 + 1456379925 z^4 + 20723056536 z^5 + 13417398813 z^6 + 64940850 z^7 - 6016725 z^8 + 331500 z^9) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-428032 + 428032 Sqrt[z] + 6119520 z - 6119520 z^(3/2) - 44206635 z^2 + 44206635 z^(5/2) + 232887655 z^3 - 232887655 z^(7/2) - 1286635350 z^4 + 1286635350 z^(9/2) - 6105623706 z^5 + 6105623706 z^(11/2) - 1770889575 z^6 + 1770889575 z^(13/2) + 121279275 z^7 - 121279275 z^(15/2) - 11536200 z^8 + 11536200 z^(17/2) + 663000 z^9 - 663000 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]