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A ROOT OF xλ + ax + b = 0 USING DEGENERATE LAMBERT W FUNCTION

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Lambert W function is the inverse function of the function L(x) = xex. And it is useful tool for finding a root of ax + bx + c = 0. The degenerate exponential function eλ(t) has been studied by many mathematicians, and numerous related results have been published. In this paper, we define the inverse function Wλ(x) of the function Lλ = xeλ(x). Taylor expansion of Wλ(x) are presented and a range of radius of convergence of the series is presented. We apply this Wλ(x) to find a root of xλ + ax + b = 0.

Abstract

Lambert W function is the inverse function of the function L(x) = xex. And it is useful tool for finding a root of ax + bx + c = 0. The degenerate exponential function eλ(t) has been studied by many mathematicians, and numerous related results have been published. In this paper, we define the inverse function Wλ(x) of the function Lλ = xeλ(x). Taylor expansion of Wλ(x) are presented and a range of radius of convergence of the series is presented. We apply this Wλ(x) to find a root of xλ + ax + b = 0.

참고문헌 (26)

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