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無限連分数の収束について
https://kitami-it.repo.nii.ac.jp/records/6184
https://kitami-it.repo.nii.ac.jp/records/6184be24ff26-0f6f-4525-9628-0587409f4527
名前 / ファイル | ライセンス | アクション |
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1-4-12.pdf (2.6 MB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2007-04-09 | |||||
タイトル | ||||||
タイトル | 無限連分数の収束について | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
その他のタイトル | ||||||
その他のタイトル | On Convergence of Infinite Continued Fractions | |||||
著者 |
礒部, 煕郎
× 礒部, 煕郎 |
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著者別名 | ||||||
識別子 | 31696 | |||||
識別子Scheme | WEKO | |||||
姓名 | Kiro, lSOBE | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | Let {ν_k} be a sequence of natural numbers. The following form (1) of the sequence {ν_k} is called a infinite continued fraction. 1/(ν_1+1)/(ν_2+1)/(…) (1) From the sequence {ν_k} j the sequence {ξ_k}is made as follows (ξ_k=1)/(ν_1+1)/(…)/1/(ν_k-1+1)/(ν-1) (2) and it is convergent sequence. In this paper, we give the following relationsξ_2<ξ_4<…<<ξ_3<ξ_1 (9) │ξ-k-ξ-k1│<__-1/(k(k-1) (8) The conclusion drawn from these relations is the uniformity about convergence of infinite continued fractions. Namely, for any positive number s and sequence of natural numbers ε and sequence of natural numbers {ν_k}, there exists some natural number N such that N≦k, l implies │ξ-k-ξ-1│<εFurthermore, let S be the totality of all sequences of natural numbers and R be the totality of all irrational numbers in the open interval (0,I). We define the metric function d in the space S as follows d(a, b)=1/(Min{k:ν_k≠μ_k} (S∋a, b, a={ν_k}, b={μ_k}). Thespace R is the subspace of the real line. In this paper, the relations between the spaces S and R are discussed. | |||||
書誌情報 |
北見工業大学研究報告 巻 1, 号 4, p. 109-117, 発行日 1966-03 |
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フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
著者版フラグ | ||||||
値 | publisher | |||||
出版者 | ||||||
出版者 | 北見工業大学 |