radius of convergenceとは 意味・読み方・使い方

名詞

radius of convergence (plural radii of convergence)

1. for a power series ${\displaystyle \sum _{n=0}^{\infty }c_{n}(z-a)^{n}}$, the unique number ${\displaystyle R=[0,\infty ]}$ such that the sum is convergent for <math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |z-a| | z − a | < R {\displaystyle |z-a| <img loading="lazy" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48a49f86c4ae2319035fe69ebfa9883f6a0333e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.314ex; height:2.843ex;" alt="{\displaystyle |z-a|, and divergent for ${\displaystyle |z-a|>R}$

   関連する語

   • power series
   • interval of convergence