Fonksyon lanmbda Liouville

Fonksyon Lanmbda Liouville lye avèk fonksyon Omega

Fonksyon $\Omega$

$\Omega \left(n\right)=\alpha _{1}+\alpha _{2}+.....+\alpha _{i}+......+\alpha _{r-1}+\alpha _{r}$
si

$n=\left(p_{1}\right)^{{\alpha }_{1}}\times \left(p_{2}\right)^{{\alpha }_{2}}\times .....\left(p_{i}\right)^{{\alpha }_{i}}\times .....\times \left(p_{r-1}\right)^{{\alpha }_{r-1}}\times \left(p_{r}\right)^{{\alpha }_{r}}$

Fonksyon Liouville

$\lambda \left(n\right)=\left(-1\right)^{\left(\alpha _{1}+\alpha _{2}+.....+\alpha _{i}+......+\alpha _{r-1}+\alpha _{r}\right)}$
si

$n=\left(p_{1}\right)^{{\alpha }_{1}}\times \left(p_{2}\right)^{{\alpha }_{2}}\times .....\left(p_{i}\right)^{{\alpha }_{i}}\times .....\times \left(p_{r-1}\right)^{{\alpha }_{r-1}}\times \left(p_{r}\right)^{{\alpha }_{r}}$

Ekspresyon fonksyon $\lambda$ Liouville selon Lainé Jean Lhermite Junior

$\lambda \left(n\right)=\left(-1\right)^{\left(\sum _{j=1}^{n}\left({\sum _{i=1}^{n}{\left({{\left[{\frac {\left[{\frac {n}{i^{j}}}\right]}{\left({\frac {n}{i^{j}}}\right)}}\right]}\times \left(1-\left[{\frac {\left[{\frac {\left(i!\right)^{2}}{i^{3}}}\right]}{\frac {\left(i!\right)^{2}}{i^{3}}}}\right]\right)}\right)}}\right)\right)}$

Gade tou

Referans

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