equações Graceli [9]

p = progressão.

k = variável complexa.

$f(x)={\frac {1}{\pi (1+x^{2})}}\,$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

${\frac {{\bigl |}f^{(n)}(c){\bigr |}}{n!}}\leqslant {\frac {\sup _{|z-c|=r}|f(z)|}{r^{n}}}\cdot$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$c_{n}=\sum _{k=0}^{n}a_{k}b_{n-k}.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\sum _{n=0}^{\infty }a_{n},\qquad \sum _{n=0}^{\infty }b_{n},$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left(\sum _{n=0}^{\infty }a_{n}\right)\cdot \left(\sum _{n=0}^{\infty }b_{n}\right)=\sum _{n=0}^{\infty }c_{n},\qquad \mathrm {donde} \ c_{n}=\sum _{k=0}^{n}a_{k}b_{n-k}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\sum _{n=0}^{\infty }c_{n}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left(\sum _{n=0}^{\infty }a_{n}\right)\left(\sum _{n=0}^{\infty }b_{n}\right)$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$f(z_{0})={\frac {1}{2\pi i}}\oint \limits _{C}{f(z) \over z-z_{0}}\,dz$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left.{\frac {d^{n}f}{dz^{n}}}\right|_{z=z_{0}}={\frac {n!}{2\pi i}}\oint \limits _{C}{f(z) \over (z-z_{0})^{n+1}}\,dz.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

p = progressão.

k = variável complexa.

$f(x)={\frac {1}{\pi (1+x^{2})}}\,$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

${\frac {{\bigl |}f^{(n)}(c){\bigr |}}{n!}}\leqslant {\frac {\sup _{|z-c|=r}|f(z)|}{r^{n}}}\cdot$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$c_{n}=\sum _{k=0}^{n}a_{k}b_{n-k}.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\sum _{n=0}^{\infty }a_{n},\qquad \sum _{n=0}^{\infty }b_{n},$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left(\sum _{n=0}^{\infty }a_{n}\right)\cdot \left(\sum _{n=0}^{\infty }b_{n}\right)=\sum _{n=0}^{\infty }c_{n},\qquad \mathrm {donde} \ c_{n}=\sum _{k=0}^{n}a_{k}b_{n-k}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\sum _{n=0}^{\infty }c_{n}$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left(\sum _{n=0}^{\infty }a_{n}\right)\left(\sum _{n=0}^{\infty }b_{n}\right)$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$f(z_{0})={\frac {1}{2\pi i}}\oint \limits _{C}{f(z) \over z-z_{0}}\,dz$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

$\left.{\frac {d^{n}f}{dz^{n}}}\right|_{z=z_{0}}={\frac {n!}{2\pi i}}\oint \limits _{C}{f(z) \over (z-z_{0})^{n+1}}\,dz.$ $\Gamma (t)=\int _{0}^{\infty }x^{{t-1}}e^{{-x}}dx$ cos [ $(n-1)!={\frac {n!}{n}}$ ] / pk [ $\zeta (s)=\sum _{k=1}^{\infty }k^{-s}.$ ] dx=

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equações Graceli [9]

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