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nice-calculus-evaluate-lim-s-0-1-s-1-s-2-euler-mascheroni-constant-m-n-1970-




Question Number 118438 by mnjuly1970 last updated on 17/Oct/20
      ...  nice  calculus...         evaluate ::                     lim_(s→0) ((ζ( 1+s )+ζ(1−s))/2) =^? γ              γ: euler−mascheroni constant     m.n.1970.
$$\:\:\:\:\:\:…\:\:{nice}\:\:{calculus}… \\ $$$$ \\ $$$$\:\:\:\:\:{evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$${lim}_{{s}\rightarrow\mathrm{0}} \frac{\zeta\left(\:\mathrm{1}+{s}\:\right)+\zeta\left(\mathrm{1}−{s}\right)}{\mathrm{2}}\:\overset{?} {=}\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant} \\ $$$$\:\:\:{m}.{n}.\mathrm{1970}. \\ $$$$ \\ $$

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