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Can $\{n!\log n\}$ converge to $1$?

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#real-analysis #number-theory #limits #factorial #fractional-part
188
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Integrals involving the fractional part function and the W-Lambert function

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#proof-verification #definite-integrals #closed-form #lambert-w #fractional-part
242
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Prove that $ \left\lfloor{\frac xn}\right\rfloor= \left\lfloor{\lfloor{x}\rfloor\over n}\right\rfloor$ where $n \ge 1, n \in \mathbb{N}$

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#functions #ceiling-and-floor-functions #fractional-part
296
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Double fractional part integral

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#integration #sequences-and-series #definite-integrals #fractional-part
320
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Square root of fractional part integral

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#integration #zeta-functions #fractional-part
267
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Fractional part of the floor function Integral

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#integration #sequences-and-series #riemann-zeta #euler-mascheroni-constant #fractional-part
203
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How is it possible to solve a second degree polynomial combined with a modulo?

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#algebra-precalculus #polynomials #modular-arithmetic #fractional-part
348
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limit of sequence involving the fractional part

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#sequences-and-series #limits #fractional-part
185
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symmetric double-integral on fractional part

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#definite-integrals #riemann-zeta #fractional-part
113
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Variant of Stieltjes constants

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#sequences-and-series #definite-integrals #fractional-part #stieltjes-constants
444
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Evaluation of $\int_{0}^{1}\int_{0}^{1}\{\frac{1}{\,x}\}\{\frac{1}{x\,y}\}dx\,dy\,$

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#definite-integrals #euler-mascheroni-constant #fractional-part
152
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Alternating series combining harmonic number and zeta values

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#definite-integrals #zeta-functions #fractional-part #euler-sums
80
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Solve for $x$ in the equation containing ${\lfloor{x}\rfloor}$ and $\{x\}$

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#functions #ceiling-and-floor-functions #fractional-part
138
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Value of $\lim_{n\to \infty} \frac{1}{2^n} \sum_{k=1}^{2^n} \{\log_{2}k\}$

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#logarithms #fractional-part
454
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Closed form of integral over fractional part $\int_0^1 \left\{\frac{1}{2}\left(x+\frac{1}{x}\right)\right\}\,dx$

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#integration #summation #asymptotics #bessel-functions #fractional-part

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