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Derivative power rule conditions

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#calculus #derivatives #euler-mascheroni-constant
219
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Proving that the constant in Mertens' third theorem is $e^{-\gamma}$

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#prime-numbers #asymptotics #analytic-number-theory #riemann-zeta #euler-mascheroni-constant
167
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Proving the convergence of an infinite product

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#limits #taylor-expansion #binomial-theorem #infinite-product #euler-mascheroni-constant
126
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Why does Euler's number occur in the Chudnovsky Formula for calculating $\pi$?

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#pi #modular-forms #euler-mascheroni-constant
38
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Calculating large exponential shares / probabilities

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#probability #algorithms #exponentiation #approximation #euler-mascheroni-constant
95
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How to show that the integral $\int_0^1 \ln(1-x^{1/n})dx=-\sum_{k=1}^n\frac{1}{k}$

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#calculus #integration #harmonic-numbers #euler-mascheroni-constant
37
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Distributional integral involving $\frac{e^{i\omega x}}{\omega}$

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#complex-analysis #improper-integrals #distribution-theory #gamma-function #euler-mascheroni-constant
1.5k
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An approximation related to Euler's constant and the Harmonic number

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#real-analysis #asymptotics #harmonic-numbers #euler-mascheroni-constant
709
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Closed form of Euler-type sum over zeta functions $\sum _{k=2}^{\infty } \frac{\zeta (k)}{k^2}$?

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#summation #riemann-zeta #harmonic-numbers #euler-mascheroni-constant
2.1k
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How do I prove that this limit is equal to e without L'Hospital?

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#limits #limits-without-lhopital #euler-mascheroni-constant
62
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Is the number $1.201~943\dots$ of any significance?

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#functions #constants #euler-mascheroni-constant
40
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Evaluating a limit to get an integral for Euler's Constant

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#integration #number-theory #limits #euler-mascheroni-constant
67
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Relationships between irrational numbers

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#irrational-numbers #pi #euler-mascheroni-constant
89
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A question about the constant in $\sum_{2\leqslant n\leqslant x}\frac{1}{n\log n}=\log(\log x)+B+O\left(\frac{1}{x\log x}\right)$

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#proof-writing #asymptotics #analytic-number-theory #euler-mascheroni-constant
53
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Using pentration with non-integer values: how to solve 2^^^1.5?

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#euler-mascheroni-constant #hyperoperation

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