Question

How get a good approximation of integrals involving the gamma function, exponentials and the fractional part?

score 113 · Answer 1 · 2026-05-07 11:29:11

113

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How get a good approximation of integrals involving the gamma function, exponentials and the fractional part?

Published on 07 May 2026 - 11:29

score 725 · Answer 2 · 2026-05-05 11:23:36

725

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Compute a division with integer and fractional part

Published on 05 May 2026 - 11:23

score 221 · Answer 3 · 2026-05-07 13:49:17

221

Views

Justify an approximation of $\int_{0}^1\binom{ \left\{ 1/z\right\}}{z}dz$, where $ \left\{ z \right\}$ denotes the fractional part function

Published on 07 May 2026 - 13:49

score 98 · Answer 4 · 2026-05-04 08:39:54

98

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Fractional part of integer multiples

Published on 04 May 2026 - 8:39

score 152 · Answer 5 · 2026-05-07 11:34:09

152

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The behaviour of $\sum_{\mathcal{R}\leq x}\left\{\frac{x}{\mathcal{R}}\right\}$, where $\mathcal{R}$ denote Ramanujan primes

Published on 07 May 2026 - 11:34

score 145 · Answer 6 · 2026-04-29 12:24:44

145

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For $k\in\mathbb{R}$, evaluate $\lim\limits_{n \to \infty} (\sqrt{n^2+nk+1}-\lfloor \sqrt{n^2+nk+1} \rfloor)$

Published on 29 Apr 2026 - 12:24

score 147 · Answer 7 · 2026-05-07 11:27:29

147

Views

Inequality involving power to fractional part of integer multiples of logarithm of integer to coprime base.

Published on 07 May 2026 - 11:27

score 110 · Answer 8 · 2026-05-01 10:20:55

110

Views

How to show $a^{\frac{1}{b}}-c^{\frac{1}{d}}$ is rational if and only if $a^{\frac{1}{b}}$ and $c^{\frac{1}{d}}$ are rational and not equal.

Published on 01 May 2026 - 10:20

score 436 · Answer 9 · 2026-05-10 07:46:54

436

Views

How to integrate the "fractional part"/sawtooth function?

Published on 10 May 2026 - 7:46

score 163 · Answer 10 · 2026-05-10 12:06:31

163

Views

$\lim_{n \to \infty}\left \langle \sqrt{n} \right \rangle $ doesn't exist

Published on 10 May 2026 - 12:06

score 169 · Answer 11 · 2026-04-29 12:25:13

169

Views

Find the real values of $x$ that satisfy the equation $7[x]+23\{x\}=191$

Published on 29 Apr 2026 - 12:25

score 110 · Answer 12 · 2026-05-10 11:20:05

110

Views

On continuity of floor, modulus and fractional part function.

Published on 10 May 2026 - 11:20

score 872 · Answer 13 · 2026-05-10 11:18:28

872

Views

Limit involving Series and Greatest Integer Function

Published on 10 May 2026 - 11:18

score 185 · Answer 14 · 2026-05-10 11:21:51

185

Views

Integral $\int_{0}^{1}\int_{0}^{1}\sin\big\{ \tfrac{x}{y} \big\}\sin\big\{ \tfrac{y}{x} \big\}dxdy$

Published on 10 May 2026 - 11:21

score 125 · Answer 15 · 2026-05-10 11:20:52

125

Views

An approximation of a definite integral involving the Gudermannian function and the fractional part function

Published on 10 May 2026 - 11:20

List Question

How get a good approximation of integrals involving the gamma function, exponentials and the fractional part?

Compute a division with integer and fractional part

Justify an approximation of $\int_{0}^1\binom{ \left\{ 1/z\right\}}{z}dz$, where $ \left\{ z \right\}$ denotes the fractional part function

Fractional part of integer multiples

The behaviour of $\sum_{\mathcal{R}\leq x}\left\{\frac{x}{\mathcal{R}}\right\}$, where $\mathcal{R}$ denote Ramanujan primes

For $k\in\mathbb{R}$, evaluate $\lim\limits_{n \to \infty} (\sqrt{n^2+nk+1}-\lfloor \sqrt{n^2+nk+1} \rfloor)$

Inequality involving power to fractional part of integer multiples of logarithm of integer to coprime base.

How to show $a^{\frac{1}{b}}-c^{\frac{1}{d}}$ is rational if and only if $a^{\frac{1}{b}}$ and $c^{\frac{1}{d}}$ are rational and not equal.

How to integrate the "fractional part"/sawtooth function?

$\lim_{n \to \infty}\left \langle \sqrt{n} \right \rangle $ doesn't exist

Find the real values of $x$ that satisfy the equation $7[x]+23\{x\}=191$

On continuity of floor, modulus and fractional part function.

Limit involving Series and Greatest Integer Function

Integral $\int_{0}^{1}\int_{0}^{1}\sin\big\{ \tfrac{x}{y} \big\}\sin\big\{ \tfrac{y}{x} \big\}dxdy$

An approximation of a definite integral involving the Gudermannian function and the fractional part function

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