Equações Matemáticas

S(λ) = \frac{2πc^{2}h}{λ^{5}} \frac{1}{e^{hc/λKT} − 1}  (1)

S^{2} = \frac{∑_{i=1}^{n}(x_{i} − x̄)^{2}}{n − 1}  (2)

P (\overline{A ∪ B ∪ C}) = 1 − P (A ∩ B ∩ C)  (3)

σ^{2} = ∫_{−∞}^{∞}(x − μ)^{2}f(x) dx  (4)

f(x) = \frac{Γ(\frac{u+v}{2})(\frac{u}{v})^{\frac{u}{2}} x^{(u/2)−1}}{Γ(\frac{u}{2})Γ(\frac{v}{2})[(\frac{u}{v})x + 1]^{\frac{(u+v)}{2}}} , 0 < x < ∞  (5)

\frac{∂(sin ϕ)}{∂ϕ}|_{x=0} = 0  (6)

∇ ≡ i\frac{∂}{∂x} + j\frac{∂}{∂y} + k\frac{∂}{∂z}  (7)

\frac{∂θ}{∂x} = \{ \begin{matrix}0 & para x = 0 \\ −\frac{hθ}{K} & para x = b \end{matrix}  (8)

1. \begin{equation}
S(\lambda)=\frac{2\pi c^{2}h}{\lambda^{5}}\frac{1}{e^{hc/\lambda
KT}-1}
\end{equation}
2. \begin{equation}
S^2 = \frac{\sum_{i=1}^{n}(x_{i}-\bar{x})^{2}}{n-1}
\end{equation}
3. \begin{equation}
P(\overline{A\cup B\cup C})= 1 - P(A\cap B\cap C)
\end{equation}
4. \begin{equation}
\sigma^{2}=\int_{-\infty}^{\infty} (x-\mu)^{2}f(x)\,dx
\end{equation}
5. \begin{equation}
f(x)=\frac{\Gamma
(\frac{u+v}{2})(\frac{u}{v})^{\frac{u}{2}}x^{(u/2) - 1}}
 {\Gamma(\frac{u}{2})\Gamma(\frac{v}{2})[(\frac{u}{v})x + 1]^{\frac{(u
 +v)}{2}}}, \;\;\;\;0<x<\infty
\end{equation}
6. \begin{equation}
\left.\frac{\partial (\sin \phi)}{\partial \phi}\right|_{x=0} = 0
\end{equation}
7. \begin{equation}
\nabla \equiv \textbf{i}\frac{\partial}{\partial x} +
\textbf{j}\frac{\partial}{\partial y} +
\textbf{k}\frac{\partial}{\partial z}
\end{equation}
8. \begin{equation}
    \frac{\partial \theta}{\partial x}= \left\{ \begin{array}{cc}
      0 & \mbox{para x = 0} \\
      -\frac{h\theta}{K} & \mbox{para x = b} \\
    \end{array}\right.
\end{equation}