数学公式测试

2021-09-13 01:02:02

f(x0)=limΔx0ΔyΔx=limΔx0f(x0+Δx)f(x0)Δx{\color{red}f'(x_0)}={\color{green}\lim\limits_{\Delta{x}\to0}\frac{\Delta{y}}{\Delta{x}}}={\color{blue}\lim_{\Delta{x}\to0}\frac{f(x_0+\Delta{x})-f(x_0)}{\Delta{x}}}

Pkn=n!(nk)!{\displaystyle P_{k}^{n}={\frac {n!}{(n-k)!}}}

Pkn=n!(nk)!{\displaystyle P_{k}^{n}={\frac {n!}{(n-k)!}}}

Ckn=(nk)=Pknk!=n!k!(nk)!{\displaystyle C_{k}^{n}={n \choose k}={\frac {P_{k}^{n}}{k!}}={\frac {n!}{k!(n-k)!}}}

C649=(496)=49!6!43!=13983816{\displaystyle C_{6}^{49}={49 \choose 6}={\frac {49!}{6!43!}}=13983816}

Hkn=Ckn+k1 {\displaystyle H_{k}^{n}=C_{k}^{n+k-1}}

H58=C58+51=C512=12!5!7!=792 {\displaystyle H_{5}^{8}=C_{5}^{8+5-1}=C_{5}^{12}={\frac {12!}{5!7!}}=792}

Fkn=Hkn {\displaystyle F_{k}^{n}=H_{k}^{n}}

fx=fξ^e2πiξxdξf\relax{x} = \int_{-\infty}^\infty{f}\hat\xi\,e^{2 \pi i \xi x}\,d\xi