SinGO主题测试KateX

E=mc2E=mc^2

E=mc2E=mc^2

c=pmsqrta2+b2c = \\pm\\sqrt{a^2 + b^2}

x>yx > y

f(x)=x2f(x) = x^2

alpha=sqrt1−e2\\alpha = \\sqrt{1-e^2}

(sqrt3x−1+(1+x)2)(\\sqrt{3x-1}+(1+x)^2)

sin(alpha)theta=sum_i=0n(xi+cos(f))\\sin(\\alpha)^{\\theta}=\\sum\_{i=0}^{n}(x^i + \\cos(f))

dfrac−bpmsqrtb2−4ac2a\\dfrac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}

displaystylefrac1Bigl(sqrtphisqrt5−phiBigr)efrac25pi=1+frace−2pi1+frace−4pi1+frace−6pi1+frace−8pi1+cdots\\displaystyle \\frac{1}{\\Bigl(\\sqrt{\\phi \\sqrt{5}}-\\phi\\Bigr) e^{\\frac25 \\pi}} = 1+\\frac{e^{-2\\pi}} {1+\\frac{e^{-4\\pi}} {1+\\frac{e^{-6\\pi}} {1+\\frac{e^{-8\\pi}} {1+\\cdots} } } }

displaystyleleft(sum_k=1na_kb_kright)2leqleft(sum_k=1na_k2right)left(sum_k=1nb_k2right)\\displaystyle \\left( \\sum\_{k=1}^n a\_k b\_k \\right)^2 \\leq \\left( \\sum\_{k=1}^n a\_k^2 \\right) \\left( \\sum\_{k=1}^n b\_k^2 \\right)

a2a^2

a2+2a^{2+2}

a_2a\_2

x_23{x\_2}^3

x_23x\_2^3

1010810^{10^{8}}

a_i,ja\_{i,j}

_nP_k\_nP\_k

c=pmsqrta2+b2c = \\pm\\sqrt{a^2 + b^2}

frac12=0.5\\frac{1}{2}=0.5

dfrackk−1=0.5\\dfrac{k}{k-1} = 0.5

dbinomnkbinomnk\\dbinom{n}{k} \\binom{n}{k}

oint_Cx3,dx+4y2,dy\\oint\_C x^3, dx + 4y^2, dy

bigcap_1npbigcup_1kp\\bigcap\_1^n p \\bigcup\_1^k p

eipi+1=0e^{i \\pi} + 1 = 0

left(frac12right)\\left ( \\frac{1}{2} \\right )

x_1,2=frac−bpmsqrtcolorRedb2−4ac2ax\_{1,2}=\\frac{-b\\pm\\sqrt{\\color{Red}b^2-4ac}}{2a}

colorBluex2+colorYellowOrange2x−colorOliveGreen1{\\color{Blue}x^2}+{\\color{YellowOrange}2x}-{\\color{OliveGreen}1}

textstylesum_k=1Nk2\\textstyle \\sum\_{k=1}^N k^2

binomnk\\binom{n}{k}

0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+cdots0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\\cdots

sum_k=1Nk2\\sum\_{k=1}^N k^2

textstylesum_k=1Nk2\\textstyle \\sum\_{k=1}^N k^2

prod_i=1Nx_i\\prod\_{i=1}^N x\_i

textstyleprod_i=1Nx_i\\textstyle \\prod\_{i=1}^N x\_i

coprod_i=1Nx_i\\coprod\_{i=1}^N x\_i

textstylecoprod_i=1Nx_i\\textstyle \\coprod\_{i=1}^N x\_i

int_13frace3/xx2,dx\\int\_{1}^{3}\\frac{e^3/x}{x^2}, dx

int_Cx3,dx+4y2,dy\\int\_C x^3, dx + 4y^2, dy

_12!Omega_34{}\_1^2!\\Omega\_3^4

f(x)=∫−∞∞f^(ξ) e2πiξx dξf(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi

(∑_k=1na_kb_k)2≤(∑_k=1na_k2)(∑_k=1nb_k2)\displaystyle \left( \sum\_{k=1}^n a\_k b\_k \right)^2 \leq \left( \sum\_{k=1}^n a\_k^2 \right) \left( \sum\_{k=1}^n b\_k^2 \right)

12[1−(12)n]1−12=sn\dfrac{ \tfrac{1}{2}[1-(\tfrac{1}{2})^n] } { 1-\tfrac{1}{2} } = s_n

1(ϕ5−ϕ)e25π=1+e−2π1+e−4π1+e−6π1+e−8π1+⋯\displaystyle \frac{1}{ \Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{ \frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} { 1+\frac{e^{-6\pi}} {1+\frac{e^{-8\pi}} {1+\cdots} } } }

f(x)=∫−∞∞f^(ξ) e2πiξx dξf(x) = \int_{-\infty}^\infty \hat f(\xi)\,e^{2 \pi i \xi x} \,d\xi

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$$
$$E=mc^2$$ 
$$E=mc^2$$
$$c = \\pm\\sqrt{a^2 + b^2}$$
$$x > y$$
$$f(x) = x^2$$
$$\\alpha = \\sqrt{1-e^2}$$
$$(\\sqrt{3x-1}+(1+x)^2)$$
$$\\sin(\\alpha)^{\\theta}=\\sum\_{i=0}^{n}(x^i + \\cos(f))$$
$$\\dfrac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}$$
$$\\displaystyle \\frac{1}{\\Bigl(\\sqrt{\\phi \\sqrt{5}}-\\phi\\Bigr) e^{\\frac25 \\pi}} = 1+\\frac{e^{-2\\pi}} {1+\\frac{e^{-4\\pi}} {1+\\frac{e^{-6\\pi}} {1+\\frac{e^{-8\\pi}} {1+\\cdots} } } }$$
$$\\displaystyle \\left( \\sum\_{k=1}^n a\_k b\_k \\right)^2 \\leq \\left( \\sum\_{k=1}^n a\_k^2 \\right) \\left( \\sum\_{k=1}^n b\_k^2 \\right)$$
$$a^2$$
$$a^{2+2}$$
$$a\_2$$
$${x\_2}^3$$
$$x\_2^3$$
$$10^{10^{8}}$$
$$a\_{i,j}$$
$$\_nP\_k$$
$$c = \\pm\\sqrt{a^2 + b^2}$$
$$\\frac{1}{2}=0.5$$
$$\\dfrac{k}{k-1} = 0.5$$
$$\\dbinom{n}{k} \\binom{n}{k}$$
$$\\oint\_C x^3, dx + 4y^2, dy$$
$$\\bigcap\_1^n p \\bigcup\_1^k p$$
$$e^{i \\pi} + 1 = 0$$
$$\\left ( \\frac{1}{2} \\right )$$
$$x\_{1,2}=\\frac{-b\\pm\\sqrt{\\color{Red}b^2-4ac}}{2a}$$
$${\\color{Blue}x^2}+{\\color{YellowOrange}2x}-{\\color{OliveGreen}1}$$
$$\\textstyle \\sum\_{k=1}^N k^2$$
$$\\binom{n}{k}$$
$$0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+\\cdots$$
$$\\sum\_{k=1}^N k^2$$
$$\\textstyle \\sum\_{k=1}^N k^2$$
$$\\prod\_{i=1}^N x\_i$$
$$\\textstyle \\prod\_{i=1}^N x\_i$$
$$\\coprod\_{i=1}^N x\_i$$
$$\\textstyle \\coprod\_{i=1}^N x\_i$$
$$\\int\_{1}^{3}\\frac{e^3/x}{x^2}, dx$$
$$\\int\_C x^3, dx + 4y^2, dy$$
$${}\_1^2!\\Omega\_3^4$$
$$
f(x) = \int_{-\infty}^\infty
    \hat f(\xi)\,e^{2 \pi i \xi x}
    \,d\xi
$$
$$\dfrac{ 
    \tfrac{1}{2}[1-(\tfrac{1}{2})^n] }
    { 1-\tfrac{1}{2} } = s_n$$
$$\displaystyle 
    \frac{1}{
        \Bigl(\sqrt{\phi \sqrt{5}}-\phi\Bigr) e^{
        \frac25 \pi}} = 1+\frac{e^{-2\pi}} {1+\frac{e^{-4\pi}} {
        1+\frac{e^{-6\pi}}
        {1+\frac{e^{-8\pi}}
         {1+\cdots} }
        } 
    }$$
$$f(x) = \int_{-\infty}^\infty
    \hat f(\xi)\,e^{2 \pi i \xi x}
    \,d\xi$$
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