List questions from fractional-part

Published on 06 Jul 2017 - 19:19

115

Views

On $\int_0^1\frac{1}{x}\operatorname{frac}\left(\frac{1}{\operatorname{gd}(x)}\right)dx$, where $\operatorname{gd}(x)$ is the Gudermannian function

Published on 22 Jul 2017 - 12:48

296

Views

Definite integral $\int_2^{343} ({x-[x]})^2 dx $

Published on 10 Aug 2017 - 8:07

3.8k

Views

Integration involving fractional part function

Published on 24 Aug 2017 - 13:30

2.1k

Views

Fractional part summation

Published on 24 Aug 2017 - 15:21

158

Views

Does $\lfloor x \rfloor.\{x\}=1$ has negative solution?

Published on 25 Aug 2017 - 18:38

64

Views

Why can't I separate the fraction inside a fraction to the outside

Published on 07 Sep 2017 - 16:11

309

Views

Fractional part summation and asymptotic expansion error

Published on 24 Sep 2017 - 22:49

4.7k

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Calculate $\int_0^7\sin\left(\frac{2\pi\cdot 3x}{5}\right)\sin\left(\frac{2\pi\cdot 15 \operatorname{frac}(x)}{8}\right)dx$

Published on 12 Oct 2017 - 13:41

62

Views

Limit of summation of fractional parts

Published on 21 Oct 2017 - 1:18

37

Views

the same convergents among 3 irrotations

Published on 21 Oct 2017 - 14:20

158

Views

Express in terms of constants and series $-\int_0^1\log\left( \left\{ x^{-1/3} \right\} \right)dx$

Published on 25 Oct 2017 - 12:18

54

Views

A question involving fractional part of a number

Published on 16 Nov 2017 - 10:53

1.5k

Views

Continuity of fractional part function for negative integers

Published on 12 Dec 2017 - 22:35

505

Views

Minimum values of the sequence $\{n\sqrt{2}\}$

Published on 27 Mar 2026 - 8:17

List Question

Functional Equation involving Fractional Part: $f(\{a+b\})=\{f(a)f(b)\}$

On $\int_0^1\frac{1}{x}\operatorname{frac}\left(\frac{1}{\operatorname{gd}(x)}\right)dx$, where $\operatorname{gd}(x)$ is the Gudermannian function

Definite integral $\int_2^{343} ({x-[x]})^2 dx $

Integration involving fractional part function

Fractional part summation

Does $\lfloor x \rfloor.\{x\}=1$ has negative solution?

Why can't I separate the fraction inside a fraction to the outside

Fractional part summation and asymptotic expansion error

Calculate $\int_0^7\sin\left(\frac{2\pi\cdot 3x}{5}\right)\sin\left(\frac{2\pi\cdot 15 \operatorname{frac}(x)}{8}\right)dx$

Limit of summation of fractional parts

the same convergents among 3 irrotations

Express in terms of constants and series $-\int_0^1\log\left( \left\{ x^{-1/3} \right\} \right)dx$

A question involving fractional part of a number

Continuity of fractional part function for negative integers

Minimum values of the sequence $\{n\sqrt{2}\}$

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