<論文>方程式 e^z=az^2の根の分布と漸近評価

概要

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With regard to the quantum scattering theory, a transcendental equation, e^z=az^2 (where a is a positive constant), is studied so as to clarify the general properties of the distribution of the roots in the complex z-plane and obtain an asymptotic expression of them. The equation is resolved into a couple of relations between real and imaginary parts of z. The relations are devised to make elementary and tractable enough to allow us to find the roots graphically and globally. It is shown that there exist an infinite number of roots of the equation. The properties of the distribution of all the roots are obtained on the basis of the relations. Moreover, an efficient and systematic way of finding their asymptotic estimates is given to yield an accurate estimate of them far from the origin of the complex plane.
北海道東海大学の論文
1997-03-25