let-x-gt-1-and-x-n-1-1-n-x-zeta-function-of-Rieman-1-calculate-lim-x-x-2-let-consider-s-x-n-2-n-n-x-n-study-the-convergence-of-s-x-and-find-a-simple-form

Tinku Tara June 4, 2023 Relation and Functions 0 Comments

Question Number 32487 by abdo imad last updated on 25/Mar/18

let x>1 and ξ(x) =Σ_(n=1) ^∞ (1/n^x ) (zeta function of Rieman) 1) calculate lim_(x→+∞) ξ(x) 2)let consider s(x)=Σ_(n=2) ^∞ ((ξ(n))/n) x^n study the convergence of s(x) and find a simple form of s(x).

$${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$$${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\ $$

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let-x-gt-1-and-x-n-1-1-n-x-zeta-function-of-Rieman-1-calculate-lim-x-x-2-let-consider-s-x-n-2-n-n-x-n-study-the-convergence-of-s-x-and-find-a-simple-form

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