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ContinuedFractionK[f,g,{i,imin,imax}]

連分数 を表す．

ContinuedFractionK[g,{i,imin,imax}]

連分数 を表す．

詳細とオプション
Details and Options Details and Options
例題  
例  
オプション  
GenerateConditions  
特性と関係  
考えられる問題  
おもしろい例題  
関連項目
関連するガイド
履歴
引用書式

ContinuedFractionK

ContinuedFractionK[f,g,{i,imin,imax}]

連分数 を表す．

ContinuedFractionK[g,{i,imin,imax}]

連分数 を表す．

詳細とオプション

例題

すべて開く すべて閉じる

例  (2)

簡単な連分数：

Wolfram Language code: ContinuedFractionK[1, {n, 1, ∞}]

連分数の 次収束：

Wolfram Language code: ContinuedFractionK[n ^ 2, {n, 1, 10}]
Wolfram Language code: ContinuedFractionK[n ^ 2, {n, 1, 20}]

オプション  (1)

GenerateConditions  (1)

連分数が収束するために必要な条件を求める：

Wolfram Language code: ContinuedFractionK[a , {n, 1, ∞}, GenerateConditions -> True]

特性と関係  (2)

連分数は，二次の漸化式と解の比として構築することができる：

Wolfram Language code: rec = v[n + 1] == b[n] v[n] + a[n] v[n - 1];
Wolfram Language code: u[m_, {v0_, v1_}] := First[RecurrenceTable[rec && v[0] == v0 && v[1] == v1, v, {n, m + 1, m + 1}]]

連分数は，線形独立の2つの解の比である：

Wolfram Language code: Table[(u[m, {1, 0}]/u[m, {0, 1}]) - ContinuedFractionK[a[n], b[n], {n, m}], {m, 6}]

ContinuedFractionKおよびFromContinuedFractionは，互いに逆の関係にある：

Wolfram Language code: Table[ContinuedFractionK[k ^ 6, {k, 1, n}], {n, 6}]
Wolfram Language code: Table[FromContinuedFraction[Table[k ^ 6, {k, 1, n}]], {n, 6}]
Wolfram Language code: % == 1 / %%

考えられる問題  (1)

連分数は収束しないことがある：

Wolfram Language code: ContinuedFractionK[1 / n ^ 2, {n, 1, ∞}]

おもしろい例題  (1)

連分数の表を作る：

Wolfram Language code: flist = {{Cos[n], Sin[n], {n, 3}}, {1, 1 + n, {n, 1, a}}, {1, 1, {n, 1, ∞}}, {n, n, {n, 1, ∞}}, {n^2, 1 + 2 n, {n, 1, ∞}}, {1 + Mod[n, 2], {n, 1, ∞}}};
Wolfram Language code: Grid[Join[{{Text["Continued Fraction"], Text["Product"]}}, Transpose[{Inactive@ContinuedFractionK@@@flist, Map[ContinuedFractionK@@#&, flist]}]], IconizedObject[«Grid options»]]//TraditionalForm
Wolfram Research (2008), ContinuedFractionK, Wolfram言語関数， https://reference.wolfram.com/language/ref/ContinuedFractionK.html.

テキスト

Wolfram Research (2008), ContinuedFractionK, Wolfram言語関数， https://reference.wolfram.com/language/ref/ContinuedFractionK.html.

CMS

Wolfram Language. 2008. "ContinuedFractionK." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ContinuedFractionK.html.

APA

Wolfram Language. (2008). ContinuedFractionK. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ContinuedFractionK.html

BibTeX

@misc{reference.wolfram_2026_continuedfractionk, author="Wolfram Research", title="{ContinuedFractionK}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/ContinuedFractionK.html}", note=[Accessed: 07-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_continuedfractionk, organization={Wolfram Research}, title={ContinuedFractionK}, year={2008}, url={https://reference.wolfram.com/language/ref/ContinuedFractionK.html}, note=[Accessed: 07-August-2026]}