List of Mathematical Constants

Name
Symbol
Value
zero
0
0
one, unity
1
1
Imaginary unit, unit imaginary number
\(i\)
\(\sqrt{-1}\)
Pi, Archimedes constant or Ludolphs' number
\(\pi\)
3.14159 26535 89793 23846 26433 83279 50288
Naperian (natural) logarithm base
e
2.71828 18284 59045 23536 02874 71352 66249
Pythagoras' constant, square root of 2
\(\sqrt{2}\)
1.41421 35623 73095 04880 16887 24209 69807
Theodorus' constant, square root of 3
\(\sqrt{3}\)
1.73205 08075 68877 29352 74463 41505 87236
square root of 5
\(\sqrt{5}\)
2.23606 79774 99789 69640 91736 68731 27623
Naperian (natural) logarithm of two
\(\mathrm{ln} 2\)
0.69314718056
Naperian (natural) logarithm of ten
\(\mathrm{ln} 10\)
2.30258509299
Briggsian (common) logarithm of two
\(\mathrm{log}_{10} 2\)
0.30102999566
deBruijn-Newman Constant
\(\Lambda\)
\(0 \leq \Lambda \leq 0.22\)
Euler–Mascheroni constant
\(\gamma\)
0.57721 56649 01532 86060 65120 90082 40243
Gold ratio
\(\phi\)
1.61803 39887 49894 84820 45868 34365 63811
Meissel Mertens Constant
\(M_1\)
0.26149 72128 47642 78375 54268 38608 69585
Bernstein's constant
\(\beta\)
0.28016 94990 23869 13303
Gauss-Kuzmin-Wirsing constant
\(\lambda\)
0.30366 30028 98732 65859 74481 21901 55623
Hafner-Sarnak-McCurley constant
\(\sigma\)
0.35323 63718 54995 98454 35165 50432 68201
Landau's constant
\(L\)
0.5
Omega constant
\(\Omega\)
0.56714 32904 09783 87299 99686 62210 35554
Golomb-Dickman constant
\(\lambda, \mu\)
0.62432 99885 43550 87099 29363 83100 83724
Cahen's constnat
0.64341 05462
Twin prime constnat
\(C_2\)
0.66016 18158 46869 57392 78121 10014 55577
Laplace limit
0.66274 34193 49181 58097 47420 97109 25290
Embree-Trefethen constant
\(\beta^*\)
0.70258
Landau-Ramanujan constant
\(\mathrm{K}\)
0.76422 36535 89220 66299 06987 31250 09232
Brun's constnat for prime quadruplets
\(B_4\)
0.87058 838
Catalan's constnat
\(\mathrm{K}\)
0.91596 55941 77219 01505 46035 14932 38411
Legendre's constant
\(B_L^{'}\)
1
Viswanath's constant
\(\mathrm{K}\)
1.13198 824
Apery's constant
\(\zeta(3)\)
1.20205 69031 59594 28539 97381 61511 44999
Conway's constant
\(\lambda\)
1.30357 72690 34296 39125 70991 12152 55189
Mills' constant
\(\theta\)
1.30637 78838 63080 69046 86144 92602 60571
Plastic constant
\(\rho\)
1.32471 79572 44746 02596 09088 54478 09734
Ramanujan-Soldner constant
\(\mu\)
1.45136 92348 83381 05028 39684 85892 02744
Backhouse's constant
\(\)
1.45607 49485 82689 67139 95953 51116 54356
Porter's constant
\(\)
1.46707 80794
Lieb's square ice constant
\(\)
1.53960 07178
Erdos-Borwein constant
\(E_B\)
1.60669 51524 15291 76378 33015 23190 92458
Niven's constant
\(\)
1.70521 11401 05367 76428 85514 53434 50816
Brun's constant for twin primes
\(B_2\)
1.90216 05831 04
Universal parabolic constant
\(P_2\)
2.29558 71493 92638 07403 42980 49189 49039
Feigenbaum constant
\(\alpha\)
2.50290 78750 95892 82228 39028 73218 21578
Sierpinski's constant
\(\mathrm{K}\)
2.58498 17595 79253 21706 58935 87383 17116
Khinchin's constant
\(\)
2.68545 20010 65306 44530 97148 35481 79569
Frasen-Robinson constant
\(\mathrm{F}\)
2.80777 02420 28519 36522 15011 86557 77293
Levy's constant
\(\)
3.27582 29187 21811 15978 76818 82453 84386
Reciprocal Fibonacci constant
\(\psi\)
3.35988 56662 43177 55317 20113 02918 92717
Feigenbaum constant
\(\delta\)
4.66920 16091 02990 67185 32038 20466 20161

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