let-x-n-1-1-n-x-with-x-gt-1-prove-that-x-p-prime-1-1-p-x-

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 62003 by maxmathsup by imad last updated on 13/Jun/19

let ξ(x) =Σ_(n=1) ^∞ (1/n^x ) with x>1 prove that ξ(x) =Π_(p prime) (1/(1−p^(−x) ))

$${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{with}\:{x}>\mathrm{1}\:\:{prove}\:{that}\:\:\xi\left({x}\right)\:=\prod_{{p}\:{prime}} \:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{x}} } \\ $$

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let-x-n-1-1-n-x-with-x-gt-1-prove-that-x-p-prime-1-1-p-x-

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