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Plot of the Bring radical for real argument. In algebra, the Bring radical or ultraradical of a real number a is the unique real root of the polynomial + +.. 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 such that the Bring radical is real-valued for real a and is an ...
Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.. Solving linear, quadratic, cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions.
This formula applies to any algebraic equation of any degree without need for a Tschirnhaus transformation or any other manipulation to bring the equation into a specific normal form, such as the Bring–Jerrard form for the quintic. However, application of this formula in practice is difficult because the relevant hyperelliptic integrals and ...
This is the case, for example, for the Bring radical, which is the function implicitly defined by f ( x ) 5 + f ( x ) + x = 0 {\displaystyle f(x)^{5}+f(x)+x=0} . In more precise terms, an algebraic function of degree n in one variable x is a function y = f ( x ) , {\displaystyle y=f(x),} that is continuous in its domain and satisfies a ...
F. G. Mehler, student of Dirichlet (Ferdinand): Mehler's formula, Mehler–Fock formula, Mehler–Heine formula, Mehler functions. Meijer G-function; Josef Meixner: Meixner polynomial, Meixner-Pollaczek polynomial; Mittag-Leffler: Mittag-Leffler polynomials. Mott polynomial
This paragraph suggested that –1 is a branch point of the Bring radical and that this is the unique branch point. This appears to be wrong, the branch points being the fourth roots of –1/5. I have thus made the paragraph left precise, but, I hope, correct. By the way, has somebody considered the Bring radical for non-real a? If not, I ...
A solution in radicals or algebraic solution is an expression of a solution of a polynomial equation that is algebraic, that is, relies only on addition, subtraction, multiplication, division, raising to integer powers, and extraction of n th roots (square roots, cube roots, etc.).
Erland Samuel Bring (19 August 1736 – 20 May 1798) was a Swedish mathematician.. Bring studied at Lund University between 1750 and 1757. In 1762 he obtained a position of a reader in history and was promoted to professor in 1779.