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Question Number 62003 by maxmathsup by imad last updated on 13/Jun/19 | ||
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$${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:{with}\:{x}>\mathrm{1}\:\:{prove}\:{that}\:\:\xi\left({x}\right)\:=\prod_{{p}\:{prime}} \:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}−{p}^{−{x}} } \\ $$ | ||