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When can I assume $\operatorname{Log}$ means the natural log?

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#logarithms #euler-mascheroni-constant
326
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Proving $\lim_{n\to\infty}\sum_{k=n}^{\infty}\Big(\frac{1}{n\left\lfloor\frac kn\right\rfloor}-\frac1k\Big)=\gamma$

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#sequences-and-series #limits #summation #ceiling-and-floor-functions #euler-mascheroni-constant
168
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Where can I find a proof for $\lim\limits_{n \to \infty} \left (n - \Gamma \left( \frac 1n \right) \right) = \gamma$?

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#limits #gamma-function #euler-mascheroni-constant
375
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How to prove this limit about $\gamma=\lim_{N\to \infty }\left(\sum_{n=1}^N\frac{1}{n}-\ln N\right)$

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#calculus #sequences-and-series #analysis #limits #euler-mascheroni-constant
385
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Approximating end behavior of a function by plugging in infinity

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#limits #infinity #euler-mascheroni-constant
28
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Graph $S$ and its image $f(S)$

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#complex-analysis #graphing-functions #euler-mascheroni-constant
274
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Study and research guide on Euler–Mascheroni constant

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#analytic-number-theory #euler-mascheroni-constant #research
81
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Representation of e

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#summation #pi #euler-mascheroni-constant
89
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Is there a non-exponential function whose limit at infinity is a real, irrational number?

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#calculus #limits #polynomials #exponential-function #euler-mascheroni-constant
54
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How can an imaginary equation give a real answer?

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#euler-mascheroni-constant
186
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Deduction of 2nd order ODE general solutions

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#ordinary-differential-equations #hyperbolic-functions #euler-mascheroni-constant
249
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Characterizations of $e^x$

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#real-analysis #analysis #power-series #taylor-expansion #euler-mascheroni-constant
5k
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Implicit Euler method and explicit Euler method

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#numerical-methods #euler-mascheroni-constant #runge-kutta-methods
243
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How to prove this continued fraction connection between $\gamma$ and $e$?

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#sequences-and-series #special-functions #continued-fractions #euler-mascheroni-constant
230
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Any integral or series to prove $\frac{1}{\sqrt{3}}>\gamma$?

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#sequences-and-series #inequality #definite-integrals #euler-mascheroni-constant

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