# Llista de constants matemàtiques

Aquesta és una llista de constants matemàtiques ordenades segons la seva representació en fracció contínua:
| Nom | Conjunt de nombres | Definició o valor aproximat | Representacions en fracció contínua |
| 0 | ℕ | $0$ | [0;] |
| 1/2 | ℚ | $0.5$ | [0; 2] |
| γ | ℝ | $\lim _{n\rightarrow \infty }\left(1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+...+{\frac {1}{n}}-\ln(n)\right)$ on $ln$ representa el logaritme natural. | [0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 49, …] |
| β | ℝ | $x_{n+1}=x_{n}\pm \beta x_{n-1}\,\!$ degenera exponencialment quan $n\rightarrow \infty \,\!$ amb una probabilitat igual a 1. | [0; 1, 2, 2, 1, 3, 5, 1, 2, 6, 1, 1, 5, …] |
| K | ℝ(\ℚ ?) | $\lim _{x\rightarrow \infty }{\frac {N(x){\sqrt {\ln(x)}}}{x}}$ on $N(x)$ és el nombre de nombres naturals inferiors a $x$ que són la suma de dos quadrats. | [0; 1, 3, 4, 6, 1, 15, 1, 2, 2, 3, 1, 23, 3, 1, 1, 3, 1, 1, 7, 2, 3, 3, 18, 2, 1, 2, 1, 2, 1, 6, …] |
| B₄ | ℝ | $\left({\frac {1}{5}}+{\frac {1}{7}}+{\frac {1}{11}}+{\frac {1}{13}}\right)+\left({\frac {1}{11}}+{\frac {1}{13}}+{\frac {1}{17}}+{\frac {1}{19}}\right)+\left({\frac {1}{101}}+{\frac {1}{103}}+{\frac {1}{107}}+{\frac {1}{109}}\right)+\cdots$ | [0; 1, 6, 1, 2, 1, 2, 956, 8, 1, 1, 1, 23, …] |
| G | ℝ | ${\frac {1}{1^{2}}}-{\frac {1}{3^{2}}}+{\frac {1}{5^{2}}}-{\frac {1}{7^{2}}}+...$ | [0; 1, 10, 1, 8, 1, 88, 4, 1, 1, 7, 22, 1, 2, 3, 26, 1, 11, 1, 10, 1, 9, 3, 1, 1, 1, 1, 1, 1, 2, 2, …] |
| M | ℝ | $\lim _{n\rightarrow \infty }\left(\sum _{p\leq n}{\frac {1}{p}}-\ln(\ln(n))\right)=\gamma +\sum _{p}\left[\ln \left(1-{\frac {1}{p}}\right)+{\frac {1}{p}}\right]$ | [0; 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1, …] |
| 1 | ℕ | $1$ | [1;] |
| φ | Irracional quadràtic | ${\frac {{\sqrt {5}}+1}{2}}$ | [1; 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …] |
| E | ℝ\ℚ | $\sum _{n=1}^{\infty }{\frac {1}{2^{n}-1}}$ | [1; 1, 1, 1, 1, 5, 2, 1, 2, 29, 4, 1, 2, 2, 2, 2, 6, 1, 7, 1, 6, 2, 1, 1, 1, 20, 1, 3, 1, 1, 1, …] |
| B₂ | ℝ | $\left({\frac {1}{3}}+{\frac {1}{5}}\right)+\left({\frac {1}{5}}+{\frac {1}{7}}\right)+\left({\frac {1}{11}}+{\frac {1}{13}}\right)+\left({\frac {1}{17}}+{\frac {1}{19}}\right)+\left({\frac {1}{29}}+{\frac {1}{31}}\right)+\cdots$ | [1; 1, 9, 4, 1, 1, 8, 3, 4, 7, 1, 3, 3, 1, 2, 1, 1, 12, 4, 2, 1, 2, 2, …] |
| K | ℝ | ${\sqrt[{n}]{|f_{n}|}}\to 1,13198824\dots {\mbox{quan }}n\to \infty .$ on $f_{n}$ és una sèrie de Fibonacci aleatòria | [1; 7, 1, 1, 2, 1, 3, 2, 1, 2, 1, 17, 1, 1, 2, 1, 2, 4, 1, 2, …] |
| √2 | ℝ\ℚ | Arrel quadrada de dos | [1; 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …] |
| μ | ℝ | Únic zero positiu f de la funció logaritme integral ${\rm {li}}(x)=\int _{0}^{x}{\frac {{\rm {d}}t}{\ln(t)}}.$ | [1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, 4, 1, 12, 1, 1, 2, 2, 1, 7, 2, 1, 1, 1, 2, 30, 6, 3, 6, …] |
| 2 | ℕ | $2$ | [2;] |
| α | ℝ | ≈ 2,502 907 875 095 892 822 283 902 873 218 215 78 | [2; 1, 1, 85, 2, 8, 1, 10, 16, 3, 8, 9, 2, 1, 40, 1, 2, 3, 2, 2, 1, 17, 1, 1, 5, 3, 2, 6, 3, 5, 1, …] |
| e | ℝ\ℚ | $\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}$ | [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1, 12, 1, 1, 14, …] |
| K$_h$ | ℝ | Per $x=a_{0}+{\frac {1}{a_{1}+{\frac {1}{a_{2}+{\frac {1}{a_{3}+...}}}}}}$, es compleix gairebé sempre que $\lim _{n\rightarrow \infty }\left(\prod _{i=1}^{n}a_{i}\right)^{1/n}=K\approx 2,6854520010\dots$ | [2; 1, 2, 5, 1, 1, 2, 1, 1, 3, 10, 2, 1, 3, 2, 24, 1, 3, 2, 3, 1, 1, 1, 90, …] |
| 3 | ℕ | $3$ | [3;] |
| π | ℝ\ℚ | Producte de Wallis: ${\frac {2}{1}}\cdot {\frac {2}{3}}\cdot {\frac {4}{3}}\cdot {\frac {4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdot {\frac {8}{7}}\cdot {\frac {8}{9}}\cdots ={\frac {\pi }{2}}$ | [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, 1, 84, 2, 1, 1, 15, 3, 13, 1, 4, 2, …] |
| 4 | ℕ | $4$ | [4;] |
| δ | ℝ | ≈ 4,669 201 609 102 990 671 853 203 820 466 201 61 | [4; 1, 2, 43, 2, 163, 2, 3, 1, 1, 2, 5, 1, 2, 3, 80, 2, 5, 2, 1, 1, 1, 33, 1, 1, 53, 1, 1, 1, 1, 1, …] |

## Vegeu també

* Constant física