image
imagewidth (px) 56
1.4k
| latex_formula
stringlengths 7
153
|
---|---|
\[t(x)= \sum_{n=0}t_{n} \cos \frac{nx}{R}\] |
|
\[\frac{1}{2}p^{2}+ \frac{1}{2}m^{2}x^{2}+gx^{4}\] |
|
\[a= \frac{A- \sin^{2} \theta_{1}}{ \cos^{2} \theta_{1}}\] |
|
\[\frac{G}{H} \times \frac{G}{H}\] |
|
\[\frac{1}{ \sqrt{N}}\] |
|
\[\cos \beta_{n}\] |
|
\[\int dE\] |
|
\[\cos 2 \gamma\] |
|
\[j \neq 9\] |
|
\[v_{1}+v_{2}+ \ldots+v_{n}=nv_{n+1}\] |
|
\[8=2+2+1+1+1+1\] |
|
\[7_{ \alpha}7_{ \alpha}\] |
|
\[\sum_{a}x_{a}=1\] |
|
\[x^{ \prime}(j)=g(j)x(j)\] |
|
\[n_{1} \neq n_{2} \neq n_{3}\] |
|
\[b= \sqrt{x^{i}x^{i}}\] |
|
\[\sqrt{1+y}\] |
|
\[c_{a}(x_{a})\] |
|
\[c^{4}+c_{0}^{4}+c_{1}^{4}\] |
|
\[y= \cos(2x)\] |
|
\[(xy+yx)/2\] |
|
\[(-1)^{w_{6}+w_{7}+w_{8}+w_{9}}\] |
|
\[f(x)-1+ \sum_{n}x^{n}b_{n}(f)\] |
|
\[x^{i}+dx^{i}\] |
|
\[\cos \frac{(a_{0}-a_{1}) \pi}{2}\] |
|
\[X^{6789}=-X^{6789}\] |
|
\[e>e_{c}\] |
|
\[2^{ \frac{1}{4}}( \frac{5- \sqrt{5}}{5+ \sqrt{5}})^{ \frac{3}{4}}\] |
|
\[x^{8}+ix^{9}\] |
|
\[8+7+7+4=26\] |
|
\[\sin( \frac{2 \pi k}{p})\] |
|
\[x^{6}+ \ldots\] |
|
\[\frac{1}{g}(g-B) \frac{1}{g+B}\] |
|
\[21 \times 20 \times 8 \times 8\] |
|
\[\lim_{t \rightarrow \infty}2f_{0}(t)f_{1}(t)=0\] |
|
\[z^{ \frac{1}{6}} \log z\] |
|
\[f(x)= \sin x\] |
|
\[(ba)^{0}=a^{0}b^{0}=b^{0}a^{0}\] |
|
\[-(X^{0})^{2}+(X^{1})^{2}+(X^{2})^{2}+(X^{3})^{2}+(X^{4})^{2}= \alpha_{B}^{2}\] |
|
\[s(n)= \frac{1}{ \sqrt{2}}( \cos \frac{n \pi}{4}+ \sin \frac{n \pi}{4}) \cos \frac{n \pi}{4}\] |
|
\[\frac{(n+3)n}{(n+2)^{2}(n+1)^{2}}\] |
|
\[f_{x_{1}}(x_{2})=f_{x_{1}x_{2}}\] |
|
\[t= \sum_{a}t_{a}\] |
|
\[\sqrt{ \frac{2}{ \pi}} \cos(t- \frac{3 \pi}{4})\] |
|
\[y^{2}=ax^{4}+4bx^{3}+6cx^{2}+4dx+e\] |
|
\[\frac{2}{3}(3 \pm 4 \sqrt{6}c+4c^{2})\] |
|
\[- \frac{1}{3}+1=- \frac{2}{3}\] |
|
\[N.n\] |
|
\[y^{2}=(x-b_{1})(x-b_{2})(x-b_{3})\] |
|
\[c=c_{1}+c_{2}\] |
|
\[\sqrt{3}( \sqrt{2})\] |
|
\[- \sqrt{2(2- \sqrt{2})}\] |
|
\[\pi_{0} \pi_{0} \pi_{0}\] |
|
\[\sqrt{1-x}\] |
|
\[\lim_{r \rightarrow \infty}f(r)=0\] |
|
\[F(x)= \frac{dx}{(1-x)^{d}}- \frac{1}{(1-x)^{d}}+1\] |
|
\[1_{1}+1_{2}+1_{3}+1_{4}+3 \times 4\] |
|
\[B=- \frac{1}{4} \tan( \frac{p \pi}{2})\] |
|
\[\frac{1}{n}\] |
|
\[1 \neq 2 \neq 3\] |
|
\[x=|a-b|+1+2n\] |
|
\[\sin \gamma L\] |
|
\[-2 \int_{2}^{ \infty} \frac{dy}{ \sqrt{y^{2}-4}} \frac{1}{(y+2 \sigma_{1})^{3}}\] |
|
\[x_{o} \leq x \leq L\] |
|
\[B_{3}-2B_{6}+B_{13}+B_{17}-B_{19}=0\] |
|
\[\log p_{0}\] |
|
\[x-y\] |
|
\[\sum n_{i}\] |
|
\[y^{4}=(x-b_{1})(x-b_{1})^{2}(x-b_{3})^{2}(x-b_{4})^{3}\] |
|
\[x \rightarrow x\] |
|
\[\frac{8m(m+1)}{m+31}\] |
|
\[\sin \phi=2 \sin \frac{ \phi}{2} \cos \frac{ \phi}{2}\] |
|
\[b= \sin \alpha\] |
|
\[c= \frac{3}{2}- \frac{12}{m(m+2)}\] |
|
\[x= \sin^{2}q\] |
|
\[u_{7}=x_{7} \sqrt{x_{4}^{4}+x_{5}^{4}}\] |
|
\[x_{0}^{2}+x_{1}^{2}+x_{2}^{2}+x_{3}^{2}=1\] |
|
\[\exists g \in G\] |
|
\[\sqrt{iz}\] |
|
\[9x9\] |
|
\[+z_{2}^{2}z_{3}+z_{2}^{2}z_{4}+z_{3}^{2}z_{1}+z_{3}^{2}z_{2}+z_{3}^{2}z_{4}\] |
|
\[x_{m}= \sqrt{ \frac{ \sqrt{1+4c^{2}}-1}{2}}\] |
|
\[2.4 \times 1.2\] |
|
\[\frac{1}{ \sqrt{V}}\] |
|
\[\int fg= \int gf\] |
|
\[\log(z \log z)\] |
|
\[r= \sqrt{x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}}\] |
|
\[-b \leq x(p) \leq b\] |
|
\[\lim q_{n}= \alpha\] |
|
\[x^{2}+y^{2}+(z-bt)((z+at)^{2}-t^{2n+1})=0\] |
|
\[\pm \sqrt{3}\] |
|
\[(1-q_{12}^{2})^{2}(1-q_{13}^{2})^{2}(1-q_{23}^{2})^{2}(1-q_{12}^{2}q_{13}^{2}q_{23}^{2})\] |
|
\[x^{p-3}-x^{p}\] |
|
\[ds^{2}= \frac{1}{2}(-dt^{2}+ \frac{ \tan^{2}t}{1+ \frac{8}{9} \tan^{2}t}dx^{2})\] |
|
\[f_{0}>f>f_{1}\] |
|
\[- \sqrt{2- \sqrt{2}}\] |
|
\[y^{4}=(x-b_{1})^{2}(x-b_{2})^{3}(x-b_{3})^{3}\] |
|
\[\cos \theta X^{6}+ \sin \theta X^{2}\] |
|
\[-2 \log(2) \log(r)\] |
|
\[t \times t=1+t\] |