Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9c2)

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=-1/4

http://functions.wolfram.com/07.23.03.a9c2.01

Input Form

Hypergeometric2F1[-(19/4), -(1/4), 5, z] == (4096 (-4 (20064 + 20064 Sqrt[z] - 244948 z - 244948 z^(3/2) + 1521520 z^2 + 1521520 z^(5/2) - 7658805 z^3 - 7658805 z^(7/2) - 67762230 z^4 - 67762230 z^(9/2) - 1733082 z^5 - 1733082 z^(11/2) + 429624 z^6 + 429624 z^(13/2) - 76245 z^7 - 76245 z^(15/2) + 6630 z^8 + 6630 z^(17/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (80256 - 999856 z + 6325385 z^2 - 32090905 z^3 - 35842410 z^4 + 74172462 z^5 - 14658267 z^6 + 3583515 z^7 - 623220 z^8 + 53040 z^9) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])]))/ (466821830475 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]