EQUAÇÃO DE GRACELI [2]

f [x] = a0/ $\pi /4$ [PK] φ ψ + [ a pk cos [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw ] φ ψ + b sen [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ =

f [x] = a0/ $\pi /4$ [PK] φ ψ+ [ a pk cos [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw ] $\pi /4$ φ ψ+ b sen [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw $\pi /4$ φ ψ=

A(z)=\sum _{{n=-\infty }}^{\infty }a_{n}z^{n}\,

φ ψ

B(z)=\sum _{{n=-\infty }}^{\infty }b_{n}z^{n}

φ ψ

\sum _{{n=-\infty }}^{\infty }a_{n}b_{n}^{*}={\frac {1}{2\pi }}\int _{{-\pi }}^{\pi }A(e^{{i\phi }})B(e^{{i\phi }})^{*}d\phi \,

φ ψ

\Vert f\Vert _{L^{2}(-\pi ,\pi )}^{2}=\int _{-\pi }^{\pi }|f(x)|^{2}\,dx=2\pi \sum _{n=-\infty }^{\infty }|c_{n}|^{2}

$\left\|V\right\|^{2}=\sum _{k=1}^{n}V(k)^{2}$ .COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ

$(V_{1},V_{2})=\sum _{k=1}^{n}V_{1}(k)V_{2}(k)$ COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pwφ ψ

$\phi _{n}(k)=\left\|V_{n}\right\|^{-1}V_{n}(k)$ φ ψ

F=c_{1}\phi _{1}(k)+c_{2}\phi _{2}(k)+c_{3}\phi _{3}(k)

COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ

\delta _{mn}

(\phi _{m},\phi _{n})=\delta _{mn}

φ ψ

C_{n}=(F,\phi _{n})=\sum _{k=1}^{3}F(k)\phi _{n}(k)

COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ

\left\|f\right\|={\begin{Bmatrix}\int _{a}^{b}f(x)^{2}dx\end{Bmatrix}}^{\frac {1}{2}}

φ ψ

(f_{1},f_{2})=\int _{a}^{b}f_{1}(x)f_{2}(x)dx

φ ψ

\phi _{n}(x)=\left\|f_{n}\right\|^{-1}f_{n}(x)

φ ψ

f(x)=\sum _{n=1}^{\infty }\phi _{n}(x)\int _{a}^{b}f(\xi )\phi _{n}(\xi )d\xi

COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ

f(t)=A_{0}+\sum _{n=1}^{\infty }A_{n}\cdot \cos(w_{n}t-\theta _{n})

φ ψ

A_{0}={\frac {a_{0}}{2}},a_{n}=A_{n}\cos(\theta _{n})

φ ψ

b_{n}=A_{n}\sin(\theta _{n})

φ ψ

f(t)=\sum _{n=-\infty }^{\infty }c_{n}\,e^{iw_{n}t}

φ ψ

[PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / $\zeta (s)$ [-,+, *, / ] $\Gamma (z)$ [-,+, *, / ] $\psi _{n}(z)$ d sin φ ψ=

sen [x] + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ . sen [x] [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] pw + pφ ψ. .........

G [X] =A $\pi /4$ COS + [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] / pw φ ψ+ B SEN $\pi /4$ [PK] / [ ${{\ln(n!)} \over n}$ ] [-] [n! ] pS φ ψ .........

sendo p = progressão.

k, w = números variáveis.

n = fatorial.

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EQUAÇÃO DE GRACELI [2]

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