Question

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

score 104 · Answer 1 · 2026-03-20 04:24:45

104

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

Published on 20 Mar 2026 - 4:24

score 713 · Answer 2 · 2026-03-22 20:55:05

713

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Compute a division with integer and fractional part

Published on 22 Mar 2026 - 20:55

score 212 · Answer 3 · 2026-03-24 08:11:10

212

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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 24 Mar 2026 - 8:11

score 88 · Answer 4 · 2026-03-23 00:10:02

88

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Fractional part of integer multiples

Published on 23 Mar 2026 - 0:10

score 141 · Answer 5 · 2026-03-22 07:53:18

141

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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 22 Mar 2026 - 7:53

score 138 · Answer 6 · 2026-03-15 04:41:13

138

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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 15 Mar 2026 - 4:41

score 136 · Answer 7 · 2026-03-23 02:58:17

136

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

Published on 23 Mar 2026 - 2:58

score 100 · Answer 8 · 2026-03-22 16:43:10

100

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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 22 Mar 2026 - 16:43

score 423 · Answer 9 · 2026-03-22 12:23:55

423

Views

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

Published on 22 Mar 2026 - 12:23

score 153 · Answer 10 · 2026-03-23 02:13:28

153

Views

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

Published on 23 Mar 2026 - 2:13

score 160 · Answer 11 · 2026-03-22 17:35:12

160

Views

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

Published on 22 Mar 2026 - 17:35

score 105 · Answer 12 · 2026-03-23 16:18:18

105

Views

On continuity of floor, modulus and fractional part function.

Published on 23 Mar 2026 - 16:18

score 867 · Answer 13 · 2026-03-23 17:30:11

867

Views

Limit involving Series and Greatest Integer Function

Published on 23 Mar 2026 - 17:30

score 181 · Answer 14 · 2026-03-25 02:33:23

181

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

Published on 25 Mar 2026 - 2:33

score 120 · Answer 15 · 2026-03-24 00:17:37

120

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

Published on 24 Mar 2026 - 0:17

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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