Template:Mathematical expressions
表示
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.
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) |
解析式 (解析的表示) |
(一般)数式 |
---|---|---|---|---|---|---|
定数 | Yes | Yes | Yes | Yes | Yes | Yes |
初等算術 (四則演算) |
Yes | 除法を除き yes | Yes | Yes | Yes | Yes |
有限和 | Yes | Yes | Yes | Yes | Yes | Yes |
有限積 | Yes | Yes | Yes | Yes | Yes | Yes |
有限連分数 | Yes | No | Yes | Yes | Yes | Yes |
変数 | No | Yes | Yes | Yes | Yes | Yes |
累乗 (自然数冪) |
No | Yes | Yes | Yes | Yes | Yes |
累乗根 (自然数冪根) |
No | No | Yes | Yes | Yes | Yes |
有理数冪 | No | No | Yes | Yes | Yes | Yes |
(自然数の)階乗 | No | No | Yes | Yes | Yes | Yes |
無理数冪 | No | No | No | Yes | Yes | Yes |
対数 | No | No | No | Yes | Yes | Yes |
三角函数 | No | No | No | Yes | Yes | Yes |
逆三角函数 | No | No | No | Yes | Yes | Yes |
双曲線函数 | No | No | No | Yes | Yes | Yes |
逆双曲線函数 | No | No | No | Yes | Yes | Yes |
代数的に解けない 多項式の根 |
No | No | No | No | Yes | Yes |
ガンマ函数 (非整数の階乗) |
No | No | No | No | Yes | Yes |
ベッセル函数 | No | No | No | No | Yes | Yes |
特殊函数 | No | No | No | No | Yes | Yes |
級数(無限和) ・冪級数 |
No | No | No | No | 収束に限り yes | Yes |
無限積 | No | No | No | No | 収束に限り yes | Yes |
無限連分数 | No | No | No | No | 収束に限り yes | Yes |
極限 | No | No | No | No | No | Yes |
微分 | No | No | No | No | No | Yes |
積分 | No | No | No | No | No | Yes |