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ultraradicals

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Ultraradicals might refer to
In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial* * * * * x * * 5 * * * + * x * + * a * . * * * {\displaystyle x^{5}+x+a.} * The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen in order that the Bring radical is a function of a, which is real-valued when a is real, and is an analytic function in a neighborhood of the real line. Because of the existence of four branch points, the Bring radical cannot be defined as a function that is continuous over the whole complex plane, and its domain of continuity must exclude four branch cuts. * George Jerrard showed that some quintic equations can be solved in closed form using radicals and Bring radicals, which had been introduced by Erland Bring. * In this article, the Bring radical of a is denoted * * * * BR * ⁡ * ( * a * ) * . * * * {\displaystyle \operatorname {BR} (a).} * For real argument, it is odd, monotonically decreasing, and unbounded, with asymptotic behavior * * * * * B * R * * ( * a * ) * ∼ * − * * a * * 1 * * / * * 5 * * * * * {\displaystyle \mathrm {BR} (a)\sim -a^{1/5}} * for large * * * * a * * * {\displaystyle a} * .

Ultraradicals might refer to

In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial*
*
*
*
* x
*
* 5
*
*
* +
* x
* +
* a
* .
*
*
* {\displaystyle x^{5}+x+a.}
* The Bring radical of a complex number a is either any of the five roots of the above polynomial (it is thus multi-valued), or a specific root, which is usually chosen in order that the Bring radical is a function of a, which is real-valued when a is real, and is an analytic function in a neighborhood of the real line. Because of the existence of four branch points, the Bring radical cannot be defined as a function that is continuous over the whole complex plane, and its domain of continuity must exclude four branch cuts.
* George Jerrard showed that some quintic equations can be solved in closed form using radicals and Bring radicals, which had been introduced by Erland Bring.
* In this article, the Bring radical of a is denoted
*
*
*
* BR
* ⁡
* (
* a
* )
* .
*
*
* {\displaystyle \operatorname {BR} (a).}
* For real argument, it is odd, monotonically decreasing, and unbounded, with asymptotic behavior
*
*
*
*
* B
* R
*
* (
* a
* )
* ∼
* −
*
* a
*
* 1
*
* /
*
* 5
*
*
*
*
* {\displaystyle \mathrm {BR} (a)\sim -a^{1/5}}
* for large
*
*
*
* a
*
*
* {\displaystyle a}
* .

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