数式生成ツール
%以下の例のように任意の数字や関数を入力します．(例はクリックすると消えます) x = {-b \pm \sqrt{b^2-4ac} \over 2a}
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数式を選択
演算子
括弧
分数
論理
集合
順序/組合せ
総和/総乗
根号/指数/対数
複素数
三角関数
極限
微分
積分
ベクトル
行列
空白
表示形式
フォント/サイズ
ギリシャ文字（大文字）
ギリシャ文字（小文字）
特殊文字
アクセント
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>
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算術記号
\[ + \]
\[ - \]
\[ \pm \]
\[ \mp \]
\[ \times \]
\[ \cdot \]
\[ \ast \]
\[ \div \]
\[ / \]
\[ ! \]
関係演算子
\[ = \]
\[ \neq \]
\[ \sim \]
\[ \simeq \]
\[ \approx \]
\[ \cong \]
\[ \lt \]
\[ \le \]
\[ \ll \]
\[ \gt \]
\[ \ge \]
\[ \gg \]
幾何学記号
\[ \equiv \]
\[ \angle \]
\[ \circ \]
\[ \perp \]
\[ /\!/ \]
\[ \parallel \]
\[ \frown \]
括弧
\[ (x) \]
\[ [a] \]
\[ \{a\} \]
\[ \langle x \rangle \]
\[ \lfloor x \rfloor \]
\[ \lceil x \rceil \]
\[ \left| x \right| \]
\[ \|x\| \]
\[ ( \frac{1}{2} ) \]
\[ \left(\frac{1}{2} \right) \]
上括弧・下括弧
\[ \overbrace{a + b + c} \]
\[ \underbrace{a + b + c} \]
\[ \overbrace{a_1 + a_2 + \cdots + a_n}^{n個} \]
\[ \underbrace{a_1 + a_2 + \cdots + a_n}_{n個} \]
分数
\[ y/x \]
\[ \frac{y}{x} \]
連分数
\[ \frac{a+\frac{b+c}{d+e}}{f+g+h} \]
\[ \frac{a+\displaystyle\frac{b+c}{d+e}}{f+g+h} \]
論理記号
\[ \to \]
\[ \gets \]
\[ \Rightarrow \]
\[ \Leftarrow \]
\[ \leftrightarrow \]
\[ \Leftrightarrow \]
\[ \iff \]
\[ \equiv \]
\[ \lnot \]
\[ \land \]
\[ \lor \]
\[ \oplus \]
\[ \underline{\lor} \]
\[ \top \]
\[ \bot \]
\[ \forall \]
\[ \exists \]
\[ \not\exists\ \]
サンプル
\[ \displaystyle \lim_{x\to a}f(x)=b \]
\[ {}^\forall \varepsilon \gt 0, {}^\exists \delta \gt 0 ~~ \mathrm{s.t.} \] \[ {}^\forall x \in \mathbb{R}, 0 \gt |x-a| \gt \delta \Rightarrow |f(x)-b| \gt \varepsilon \]
集合や要素の関係
\[ \in \]
\[ \ni \]
\[ \notin \]
\[ \subset \]
\[ \supset \]
\[ \subseteq \]
\[ \supseteq \]
\[ \not\subset \]
集合の演算
\[ \cup \]
\[ \cap \]
\[ \backslash \]
\[ A^c \]
\[ \overline{A} \]
\[ \emptyset \]
ド・モルガンの法則
\[ \overline{A \cup B}=\overline{A}\cap\overline{B} \]
\[ \overline{A \cap B}=\overline{A}\cup\overline{B} \]
特別な集合
\[ \mathbb{N} \]
\[ \mathbb{Z} \]
\[ \mathbb{Q} \]
\[ \mathbb{R} \]
\[ \mathbb{C} \]
\[ \mathbb{H} \]
無限集合濃度
\[ \aleph \]
\[ \aleph_0 \]
\[ \aleph_{\alpha} \]
順列
\[ {}_n P_k \]
\[ {}_n \mathrm{P}_k \]
\[ \displaystyle {}_n P_k = n \times (n-1) \times \cdots \times (n-k+1) = \frac{n!}{(n-k)!} \]
重複順列
\[ {}_n \Pi_k \]
\[ {}_n \Pi_k = \underbrace{n \times n \times \cdots \times n}_{k} = n^k \]
組み合わせ
\[ {}_n C_k \]
\[ {}_n \mathrm{C}_k \]
\[ { n \choose k } \]
\[ \displaystyle {}_n C_k = { n \choose k } = \frac{n!}{k! (n-k)!} = \frac{{}_n P_k}{k!} \]
重複組み合わせ
\[ {}_n H_k \]
\[ {}_n \mathrm{H}_k \]
\[ \displaystyle {}_n H_k = {}_{n+k-1} C_k = \frac{(n+k-1)!}{k! (n-1)!} \]
総和
\[ \sum \]
\[ \sum_{i=1}^{n}x_i \]
\[ \displaystyle \sum_{i=1}^\infty x_i = x_1+x_2+x_3+ \cdots \]
総乗
\[ \prod \]
\[ \displaystyle \prod_{i=1}^n x_i = x_1 \times x_2 \times \cdots \times x_n \]
サンプル
\[ \displaystyle \sum_{k=1}^{n} k = \frac{1}{2}n(n+1) \]
\[ \displaystyle \sum_{k=1}^{n} k^2 = \frac{1}{6}n(n+1)(2n+1) \]
\[ \displaystyle \sum_{k=1}^{n} k^3 = \left\{ \frac{1}{2}n(n+1) \right\}^2 \]
\[ \displaystyle \sin(\pi z) = \pi z \prod_{n=1}^\infty \left( 1 - \frac{z^2}{n^2} \right) \]
\[ \displaystyle \cos(\pi z) = \prod_{n=1}^\infty \left\{ 1 - \frac{z^2}{\left( n - \frac{1}{2} \right)^2} \right\} \]
\[ \displaystyle \prod_{n=1}^\infty \frac{(2n)^2}{(2n-1)(2n+1)} = \frac{\pi}{2} \]
根号
\[ \sqrt{x} \]
\[ \sqrt[n]{x} \]
\[ \sqrt [n]{a + b} \]
指数
\[ a^x \]
\[ a^{x + y} \]
\[ a^{x^y} \]
\[ \exp(x) \]
\[ e^x \]
\[ \mathrm{e}^x \]
対数
\[ \log x \]
\[ \log_{10}x \]
\[ \log_{e}x \]
\[ \ln x \]
複素数
\[ i^2 = -1 \]
\[ \bar{z} \]
\[ \bar{\bar{z}} = z \]
\[ z = x + yi \]
\[ |z| = \sqrt{x^2 + y^2} \]
\[ \arg (z) \]
\[ z = re^{i\theta} \]
\[ \Re z \]
\[ \Im z \]
\[ \mathrm{Re} z \]
\[ \mathrm{Im} z \]
\[ \mathbb{C} \]
立法根
\[ \displaystyle \omega = \frac{-1 + \sqrt{3}i}{2} \]
\[ 1 + \omega + \omega^2 = 0 \]
三角関数
\[ \sin x \]
\[ \cos x \]
\[ \tan x \]
\[ \csc x \]
\[ \sec x \]
\[ \cot x \]
\[ \csc \theta = \frac{1}{\sin \theta} \]
\[ \sec \theta = \frac{1}{\cos \theta} \]
\[ \cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta} \]
\[ \sin^2 \theta + \cos^2 \theta =1 \]
\[ \sin (\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \]
\[ \displaystyle \tan (x \pm y) =\frac{\tan x \pm \tan y}{1 \mp \tan x \tan y} \]
逆三角関数
\[ \arcsin x \]
\[ \arccos x \]
\[ \arctan x \]
\[ \mathrm{Arcsin} x \]
\[ \mathrm{Arcsin} x \]
\[ \mathrm{Arcsin} x \]
\[ \arcsin \theta = \sin^{-1} \theta \]
\[ \arccos \theta = \cos^{-1} \theta \]
\[ \arctan \theta = \tan^{-1} \theta \]
双曲線関数
\[ \sinh x \]
\[ \cosh x \]
\[ \tanh x \]
\[ \coth x \]
\[ \displaystyle \sinh x = \frac{e^x - e^{-x}}{2} \]
\[ \displaystyle \cosh x = \frac{e^x + e^{-x}}{2} \]
\[ \displaystyle \tanh = \frac{\sinh x}{\cosh x} \]
\[ \displaystyle \coth = \frac{1}{\tanh x} \]
逆双曲線関数
\[ \sinh^{-1} x = \ln \left( x + \sqrt{x^2 + 1} \right) \]
\[ \cosh^{-1} x = \ln \left( x \pm \sqrt{x^2 - 1} \right) \]
\[ \displaystyle \tanh = \frac{1}{2} \ln \left( \frac{1 + x}{1 - x} \right) \]
極限
\[ \lim_{n \to \infty} \frac{1}{n} = 0 \]
上極限・下極限
\[ \limsup_{n \to \infty} a_n \]
\[ \liminf_{n \to \infty} a_n \]
\[ \overline{\lim}_{n \to \infty} a_n = \lim_{n \to \infty} \left( \sup_{k \ge n} a_k \right) \]
\[ \underline{\lim}_{n \to \infty} a_n = \lim_{n \to \infty} \left( \inf_{k \ge n} a_k \right) \]
ラグランジュ記法
\[ f^{\prime}(x) \]
\[ f^{\prime\prime}(x) \]
\[ f^{(n)}(x) \]
ライプニッツ記法
\[ \frac{dy}{dx} \]
\[ \frac{ \mathrm{d} y}{ \mathrm{d} x} \]
\[ \frac{d^n y}{dx^n} \]
\[ \left. \frac{dy}{dx} \right|_{x=a} \]
ニュートン記法
\[ \dot{y} = \frac{dy}{dt} = v \]
\[ \ddot{y} = \frac{d^2y}{dt^2} =a \]
オイラー記法
\[ Df \]
\[ D_x y \]
\[ f'(x) = \frac{df}{dx} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \]
偏微分
\[ \partial \]
\[ \frac{\partial f}{\partial x} =f_x \]
\[ \frac{\partial}{\partial y} \left( \frac{\partial f}{\partial x} \right) = f_{xy} \]
\[ \frac{\partial^n f}{\partial x^n} \]
ベクトルの微分演算
\[ \nabla \]
\[ \nabla = \left( \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} \right) \]
\[ \mathrm{grad} \phi = \nabla \phi \]
\[ \mathrm{div} \mathbf{A} = \nabla \cdot \mathbf{A} \]
\[ \mathrm{rot} \mathbf{A} = \nabla \times \mathbf{A} \]
\[ \Delta = \nabla^2 \]
\[ \Delta \phi = \nabla \cdot \nabla \phi = \left( \frac{\partial^2}{\partial x^2} + \frac{\partial^2}{\partial y^2} + \frac{\partial^2}{\partial z^2} \right) \phi \]
積分
\[ \int f(x)dx \]
\[ \int_0^{\infty} f(x)dx \]
\[ \begin{align*} \int_1^2 x^2 dx &= \left[ \frac{x^3}{3} \right]_1^2 \\ &= \frac{8}{3} - \frac{1}{3} \\ &= \frac{7}{3} \end{align*} \]
重積分
\[ \iint_D f(x, y)dxdy \]
\[ \iiint_V f(x, y, z)dxdydz \]
\[ \int \!\!\!\! \int_D f(x, y)dxdy \]
\[ \idotsint_D f(x_1, \cdots , x_n) dx_1 \cdots dx_n \]
周回積分
\[ \oint_C fds \]
\[ \oint_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r} \]
矢印表記
\[ \vec{a} \]
\[ \overrightarrow{AB} \]
太字表記
\[ \boldsymbol{a} \]
\[ \boldsymbol{A} \]
\[ \boldsymbol{\mathrm{e}} \]
\[ \mathbf{e} \]
行ベクトル・列ベクトル
\[ ( a_1, a_2, \cdots , a_n ) \]
\[ \left( \begin{array}{c} a_1 \\a_2 \\ \vdots \\ a_n \end{array}\right) \]
ノルム
\[ |\vec{a}| \]
\[ \| \boldsymbol{A} \| \]
\[ a = \| \boldsymbol{a} \| = \sqrt{a_1^2 + a_2^2 + \cdots +a_n^2} \]
内積(スカラー積)・外積(ベクトル積)
\[ \boldsymbol{a} \cdot \boldsymbol{b} \]
\[ \boldsymbol{a} \times \boldsymbol{b} \]
\[ ( \boldsymbol{a} , \boldsymbol{b} ) = \boldsymbol{a} \cdot \boldsymbol{b} = \sum_{i=1}^n a_i b_i \]
\[ [ \boldsymbol{a} , \boldsymbol{b} ] = \boldsymbol{a} \times \boldsymbol{b} = \sum_{j,k} \varepsilon_{ijk} a_j b_k \]
転置
\[ {}^t \boldsymbol{A} \]
\[ \boldsymbol{A}^{ \mathrm{T} } \]
\[ \boldsymbol{a} = ( a_1, a_2, \cdots , a_n )^{ \mathrm{T} } = \left( \begin{array}{c} a_1 \\ a_2 \\ \vdots \\ a_n \end{array} \right) \]
matrix環境
\[ \begin{matrix} a & b \\ c & d \end{matrix} \]
\[ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \]
\[ \begin{bmatrix} a & b \\ c & d \end{bmatrix} \]
\[ \begin{Bmatrix} a & b \\ c & d \end{Bmatrix} \]
\[ \begin{vmatrix} a & b \\ c & d \end{vmatrix} \]
\[ \begin{Vmatrix} a & b \\ c & d \end{Vmatrix} \]
\[ \begin{pmatrix}a & b & c \\ d & e & f \end{pmatrix} \]
array環境
\[ \left( \begin{array}{ccc} a & b & c \\ d & e & f \\ g & h & i \end{array} \right) \]
\[ \left[ \begin{array}{rrr} 1 & 10 & 100 \\ 10 & 100 & 1 \\ 100 & 1 & 10 \end{array} \right] \]
\[ \left( \begin{array}{crl} 1 & 10 & 100 \\ 10 & 100 & 1 \\ 100 & 1 & 10 \end{array} \right) \]
サンプル
\[ A = a_{ij} = \left( \begin{array}{cccc} a_{11} & a_{12} & \ldots & a_{1n} \\ a_{21} & a_{22} & \ldots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \ldots & a_{mn} \end{array} \right) \]
\[ \left( \begin{array}{c|cc} a & b & c \\ \hline d & e & f \\ g & h & i \end{array} \right) \]
\[ \begin{pmatrix} \lambda_1 & & & & \\ & \lambda_2 & & \Huge{0} & \\ & & \ddots & & \\ & \Huge{0} & & \lambda_{n-1} & \\ & & & & \lambda_n \end{pmatrix} \]
その他
\[ \left(\begin{array}{ccc} a & b & c\\ d & e & f \end{array}\right)^{\mathrm{T}} =\left(\begin{array}{cc} a & d \\ b & e \\ c & f \end{array}\right) \]
\[ \mathrm{tr} \begin{pmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{pmatrix} = a_{11} + a_{22} + a_{33} \]
\[ \mathrm{det} A = \begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc \]
\[ \mathrm{rank} A \]
\[ \dim A \]
空白
\[ space \]
\[ space*2 \]
\[ space*2 \]
\[ space*3/18 \]
\[ space*4/18 \]
\[ space*5/18 \]
\[ space*(-3/18) \]
複数行の数式
\[ \begin{eqnarray} x_1 + 2x_2 & = 1 \\ 2x_1 + 3x_2 & = 3 \end{eqnarray} \]
\[ \begin{align} x_1 + 2x_2 + x_3 & = 3 \\ 2x_1 + 3x_2 + 4x_3 & = 2 \\ 3x_1 + 2x_2 + x_3 & = 0 \end{align} \]
\[ \begin{align*} x^2 - (a + b)x + ab & = 0 \\ (x - a) (x - b) & = 0 \\ x & = a, b \end{align*} \]
\[ \begin{eqnarray} x_1 + 2x_2 & = & 1 \tag{1} \\ 2x_1 + 3x_2 & = & 3 \tag{2} \end{eqnarray} \]
場合分け
\[ \begin{cases} x_1 + 2x_2 + x_3 = 3 \\ 2x_1 + 3x_2 + 4x_3 = 2 \\ 3x_1 + 2x_2 + x_3 = 0 \end{cases} \]
\[ |x|= \begin{cases} x & ( x \ge 0 ) \\ -x & ( x \lt 0 ) \end{cases} \]
書体
\[ \rm ABC abc あいう \]
\[ \bf ABC abc あいう \]
\[ \it ABC abc あいう \]
\[ \sf ABC abc あいう \]
\[ \tt ABC abc あいう \]
\[ \frak ABC abc あいう \]
\[ \scr ABC abc あいう \]
\[ \mathbb{ABC abc あいう} \]
\[ \scr{AB}\bf{CD}\it{EF} \]
カリグラフィー
\[ \mathcal{ABCDEFGHIJKLMN} \mathcal{OPQRSTUVWXYZ} \]
\[ \mathcal{L}[f(t)]=\int_0^{\infty}f(t)e^{-st}dt \]
\[ \mathcal{F}[g(t)]=\int_{-\infty}^{\infty}g(t)e^{-2\pi ift}dt \]
文字サイズ
\[ \Huge Huge \]
\[ \huge huge \]
\[ \LARGE LARGE\]
\[ \Large Large \]
\[ \large large\]
\[ \normalsize normalsize \]
\[ \small small \]
\[ \scriptsize scriptsize \]
\[ \tiny tiny \]
\[ \Large{L}\normalsize{M}\small{s} \]
ギリシャ文字（大文字）
\[ \Gamma \]
\[ \varGamma \]
\[ \Delta \]
\[ \varDelta \]
\[ \Theta \]
\[ \varTheta \]
\[ \Lambda \]
\[ \varLambda \]
\[ \Xi \]
\[ \varXi \]
\[ \Pi \]
\[ \varPi \]
\[ \Sigma \]
\[ \varSigma \]
\[ \Upsilon \]
\[ \varUpsilon \]
\[ \Phi \]
\[ \varPhi \]
\[ \Psi \]
\[ \varPsi \]
\[ \Omega \]
\[ \varOmega \]
ギリシャ文字（小文字）
\[ \alpha \]
\[ \beta \]
\[ \gamma \]
\[ \delta \]
\[ \epsilon \]
\[ \varepsilon \]
\[ \zeta \]
\[ \eta \]
\[ \theta \]
\[ \vartheta \]
\[ \iota \]
\[ \kappa \]
\[ \lambda \]
\[ \mu \]
\[ \nu \]
\[ \xi \]
\[ o \]
\[ \pi \]
\[ \varpi \]
\[ \rho \]
\[ \varrho \]
\[ \sigma \]
\[ \varsigma \]
\[ \tau \]
\[ \upsilon \]
\[ \phi \]
\[ \varphi \]
\[ \chi \]
\[ \psi \]
\[ \omega \]
記号
\[ \# \]
\[ \$ \]
\[ \% \]
\[ \& \]
\[ \{ \]
\[ \} \]
\[ \_ \]
\[ \S \]
\[ \verb|<| \]
\[ \verb|>| \]
\[ \verb|^| \]
\[ \verb|~| \]
\[ \verb|\| \]
\[ \verb+|+ \]
ロゴ
\[ \TeX \]
\[ \LaTeX \]
その他特殊文字
\[ \aleph \]
\[ \hbar \]
\[ \wp \]
\[ \Re \]
\[ \Im \]
\[ \spadesuit \]
\[ \diamondsuit \]
\[ \clubsuit \]
\[ \heartsuit \]
アクセント
\[ \hat{a} \]
\[ \acute{a} \]
\[ \tilde{a} \]
\[ \bar{a} \]
\[ \dot{a} \]
\[ \check{a} \]
\[ \grave{a} \]
\[ \breve{a} \]
\[ \vec{a} \]
\[ \ddot{a} \]
複数文字に対するアクセント記号
\[ \widehat{ABC} \]
\[ \overline{ABC} \]
\[ \overrightarrow{ABC} \]
\[ \overbrace{ABC} \]
\[ \overbrace{ABC \cdots Z}^{26} \]
\[ \widetilde{ABC} \]
\[ \underline{ABC} \]
\[ \overleftarrow{ABC} \]
\[ \underbrace{ABC} \]
\[ \underbrace{ABC \cdots Z}_{26} \]
参考元：MathJax-LaTeXコマンド集【完全版】
この作成物および同梱物を使用したことによって生じたすべての障害・損害・不具合等に関しては，私と私の関係者および私の所属するいかなる団体・組織とも，一切の責任を負いません．各自の責任においてご使用ください．
制作： 273*
This software includes the work that is distributed in the Apache License 2.0.
