গাণিতিক ধ্ৰুৱকৰ তালিকা

__NOTOC__**গাণিতিক ধ্ৰুৱক**  হৈছে এনে এটা সংখ্যা যাৰ মান এটা দ্ব্যৰ্থহীন সংজ্ঞাৰ দ্বাৰা নিৰ্ধাৰণ কৰা হয়। ইয়াক প্ৰায়ে এটা চিহ্ন (যেনে, বৰ্ণমালাৰ আখৰ) বা গণিতজ্ঞসকলৰ নামেৰে উল্লেখ কৰা হয়। উদাহৰণস্বৰূপে, ধ্ৰুৱক π (পাই) ক এটা বৃত্তৰ পৰিধিৰ দৈৰ্ঘ্য আৰু ইয়াৰ ব্যাসৰ অনুপাত হিচাপে সংজ্ঞায়িত কৰিব পাৰি।

## তালিকা



*: Halted program
*: Size in bits of program 
*: Domain of all programs that stop.

|১৯৭৫
|data-sort-value="5"|<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|Robbins constant
|\Delta(3)
|0.66170 71822 67176 23515 
| \frac{4 \! + \! 17\sqrt2 \! -6 \sqrt3 \! -7\pi}{105} \! + \! \frac{\ln(1 \! + \! \sqrt2)}{5} \! + \! \frac{2\ln(2 \! + \! \sqrt3)}{5} 
|১৯৭৭
|data-sort-value="5"|<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|Weierstrass constant 
|
|0.47494 93799 87920 65033 
|\frac{2^{5/4} \sqrt{\pi} \, e^{\pi/8}}{\Gamma(\frac{1}{4})^{2}}
|data-sort-value="1978"|১৯৭৮ চনৰ আগত
|data-sort-value="5"|<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|Fransén–Robinson constant
|F
|2.80777 02420 28519 36522 
|\int_{0}^\infty \frac{dx}{\Gamma(x)} = e + \int_0^\infty \frac{e^{-x}}{\pi^2 + \ln^2 x}\, dx
|১৯৭৮
|data-sort-value="7"|
|-
|Feigenbaum constant α
|\alpha
|2.50290 78750 95892 82228 
|Ratio between the width of a tine and the width of one of its two subtines in a bifurcation diagram
|১৯৭৯
| data-sort-value="7" |
|-
|Second du Bois-Reymond constant
|C_2
|0.19452 80494 65325 11361 
|\frac{e^2-7}{2} = \int_0^\infty \left|{\frac{d}{dt}\left(\frac{\sin t}{t}\right)^2}\right|\,dt-1 
|১৯৮৩
| data-sort-value="5" |<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|Erdős–Tenenbaum–Ford constant
|\delta
|0.08607 13320 55934 20688 
|1-\frac{1+\log\log2}{\log2}
|১৯৮৪
| data-sort-value="7" |
|-
|Conway's constant
|\lambda
|1.30357 72690 34296 39125 
|Real root of the polynomial:
 \begin{smallmatrix}
x^{71}-x^{69}-2x^{68}-x^{67}+2x^{66}+2x^{65}+x^{64}-x^{63}-x^{62}-x^{61}-x^{60}\\
-x^{59}+2x^{58}+5x^{57}+3x^{56}-2x^{55}-10x^{54}-3x^{53}-2x^{52}+6x^{51}+6x^{50}\\
+x^{49}+9x^{48}-3x^{47}-7x^{46}-8x^{45}-8x^{44}+10x^{43}+6x^{42}+8x^{41}-5x^{40}\\
-12x^{39}+7x^{38}-7x^{37}+7x^{36}+x^{35}-3x^{34}+10x^{33}+x^{32}-6x^{31}-2x^{30}\\
-10x^{29}-3x^{28}+2x^{27}+9x^{26}-3x^{25}+14x^{24}-8x^{23}-7x^{21}+9x^{20}\\
+3x^{19}\!-4x^{18}\!-10x^{17}\!-7x^{16}\!+12x^{15}\!+7x^{14}\!+2x^{13}\!-12x^{12}\!-4x^{11}\!-2x^{10}\\
+5x^{9}+x^{7}-7x^{6}+7x^{5}-4x^{4}+12x^{3}-6x^{2}+3x-6\ =\ 0 \quad\quad\quad
\end{smallmatrix}
|১৯৮৭
| data-sort-value="4" |<math>\mathbb{A}</math>
|-
|Hafner–Sarnak–McCurley constant
|\sigma
|0.35323 63718 54995 98454 
| \prod_{p\text{ prime}}{\left(1- \left(1-\prod_{n\ge1}\left(1-\frac{1}{p^n}\right)\right)^2 \right)} \!

|১৯৯১
| data-sort-value="7" |
|-
|Backhouse's constant
|B
|1.45607 49485 82689 67139 
|\lim_{k \to \infty}\left | \frac{q_{k+1}}{q_k} \right \vert  \quad \scriptstyle \text {where:} \displaystyle \;\; Q(x)=\frac{1}{P(x)}= \! \sum_{k=1}^\infty q_k x^k  
 P(x) =  1+\sum_{k=1}^\infty {p_k x^k} = 1+2x+3x^2+5x^3+\cdotswhere *p<sub>k</sub>* is the *k*th prime number
|১৯৯৫
| data-sort-value="7" |
|-
|Viswanath constant
|
|1.13198 82487 943 
|\lim_{n \to \infty}|f_n|^\frac{1}{n} &nbsp;&nbsp;&nbsp;&nbsp; where *f**n* = *f**n*−1 ± *f**n*−2, where the signs + or − are chosen at random with equal probability 1/2
|১৯৯৭
| data-sort-value="7" |
|-
|Komornik–Loreti constant
|q
|1.78723 16501 82965 93301 
|Real number q such that 1 = \sum_{k=1}^\infty \frac{t_k}{q^k}, or \prod_{n=0}^\infty\left (1-\frac{1}{q^{2^n}}\right )+\frac{q-2}{q-1}=0
where *t<sub>k</sub>* is the *k*th term of the Thue–Morse sequence
|১৯৯৮
| data-sort-value="5" |<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|Embree–Trefethen constant
|\beta^{\star}
|0.70258
|
|১৯৯৯
| data-sort-value="7" |
|-
|Heath-Brown–Moroz constant
|C
|0.00131 76411 54853 17810 
|\prod_{p\text{ prime}} \left(1-\frac{1}{p}\right)^7\left(1+\frac{7p+1}{p^2}\right)
|১৯৯৯
| data-sort-value="7" |
|-
|এমআৰবি ধ্ৰুৱক
|S
|0.18785 96424 62067 12024 
| \sum_{n=1}^{\infty} (-1)^n (n^{1/n}-1) =  - \sqrt[1]{1} + \sqrt[2]{2} - \sqrt[3]{3} + \cdots
|১৯৯৯
| data-sort-value="7" |
|-
|মৌলিক ধ্ৰুৱক
|\rho
|০.৪১৪৬৮ ২৫০৯৮ ৫১১১১ ৬৬০২৪
|\sum_{p\text{ prime}} \frac{1}{2^p}= \frac{1}{4} +  \frac{1}{8} + \frac{1}{32} + \cdots
|১৯৯৯
| data-sort-value="6" |<math>\mathbb{R} \setminus \mathbb{Q}</math>
|-
|Somos' quadratic recurrence constant
|\sigma
|1.66168 79496 33594 12129 
|\prod_{n=1}^\infty n^} = 1^{1/2} \; 2^{1/4} \; 3^{1/8} \cdots 
|১৯৯৯
| data-sort-value="7" |
|-
|Foias constant
|\alpha
|1.18745 23511 26501 05459 
| x_{n+1} = \left( 1 + \frac{1}{x_n} \right)^n\text{ for }n=1,2,3,\ldots 
Foias constant is the unique real number such that if *x*1&nbsp;=&nbsp;*&alpha;* then the sequence diverges to infinity
|২০০০
| data-sort-value="7" |
|-
|Logarithmic capacity of the unit disk
|
|০.৫৯০১৭ ০২৯৯৫ ০৮০৪৮ ১১৩০২
|\frac{\Gamma(\tfrac14)^2}{4 \pi^{3/2}}
| data-sort-value="2003" |২০০৩ চনৰ আগত
| data-sort-value="5" |<math>\mathbb{R} \setminus \mathbb{A}</math>
|-
|টানিগুছি ধ্ৰুৱক
|
|০.৬৭৮২৩ ৪৪৯১৯ ১৭৩৯১ ৯৭৮০৩
| \prod_{p\text{ prime}} \left(1 - \frac{3}{p^3}+\frac{2}{p^4}+\frac{1}{p^5}-\frac{1}{p^6}\right) 
| data-sort-value="2005" |২০০৫ চনৰ আগত
| data-sort-value="7" |
|}

## ধ্ৰুৱকৰ অনুক্ৰম

## টোকা

## তথ্যসূত্ৰ


### MathWorld Wolfram.com

### OEIS.org

### OEIS Wiki

## গ্ৰন্থপঞ্জী

*  English translation by Catriona and David Lischka.
* 
* 
* 

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