Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ad2k)

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=-11/4, b>=a

For fixed z and a=-11/4, b=-5/4

http://functions.wolfram.com/07.23.03.ad2k.01

Input Form

Hypergeometric2F1[-(11/4), -(5/4), 5, z] == (4096 ((-1408 - 1408 Sqrt[z] + 16368 z + 16368 z^(3/2) - 98637 z^2 - 98637 z^(5/2) + 505428 z^3 + 505428 z^(7/2) + 5586930 z^4 + 5586930 z^(9/2) + 2376612 z^5 + 2376612 z^(11/2) + 3315 z^6 + 3315 z^(13/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-704 + 8360 z - 51315 z^2 + 264495 z^3 + 527586 z^4 - 629082 z^5 - 122655 z^6 + 3315 z^7) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (9035261235 Pi Sqrt[1 + Sqrt[z]] z^4)

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]