Template:Synthesis

The table below indicates the components that are commonly considered part of various types of mathematical expressions. With some exceptions, an expression can only have components that themselves have components of that type. For example, algebraic expressions can only have constants that are themselves algebraic, and finite sums and products in algebraic expressions can only have algebraic arguments.

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表

話

編

歴
数式の様々な表示形式とその比較
含む要素＼表示の形式算術式多項式
（多項式表示）代数式
（代数的表示）閉じた式
（閉じた表示）（英語版）解析式
（解析的表示）（一般）数式
定数YesYesYesYesYesYes
初等算術
（四則演算）Yes除法を除き yesYesYesYesYes
有限和YesYesYesYesYesYes
有限積YesYesYesYesYesYes
有限連分数YesNoYesYesYesYes
変数NoYesYesYesYesYes
累乗
（自然数冪）NoYesYesYesYesYes
累乗根
（自然数冪根）NoNoYesYesYesYes
有理数冪NoNoYesYesYesYes
（自然数の）階乗NoNoYesYesYesYes
無理数冪NoNoNoYesYesYes
対数NoNoNoYesYesYes
三角函数NoNoNoYesYesYes
逆三角函数NoNoNoYesYesYes
双曲線函数NoNoNoYesYesYes
逆双曲線函数NoNoNoYesYesYes
代数的に解けない
多項式の根（英語版）NoNoNoNoYesYes
ガンマ函数
（非整数の階乗）NoNoNoNoYesYes
ベッセル函数NoNoNoNoYesYes
特殊函数NoNoNoNoYesYes
級数（無限和）
・冪級数NoNoNoNo収束に限り yesYes
無限積NoNoNoNo収束に限り yesYes
無限連分数NoNoNoNo収束に限り yesYes
極限NoNoNoNoNoYes
微分NoNoNoNoNoYes
積分NoNoNoNoNoYes