Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ht)

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=7/4

http://functions.wolfram.com/07.23.03.a9ht.01

Input Form

Hypergeometric2F1[-(19/4), 7/4, 1, z] == (1/(21945 Pi)) (2 Sqrt[1 + Sqrt[z]] (2 (11189 - 55250 z + 94269 z^2 - 68880 z^3 + 18480 z^4) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-433 + 433 Sqrt[z] - 70871 z + 70871 z^(3/2) + 217560 z^2 - 217560 z^(5/2) - 220080 z^3 + 220080 z^(7/2) + 73920 z^4 - 73920 z^(9/2)) 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]