Mathematical constant

From Wikipedia, the free reference book

A numerical steady is an exceptional number, normally a true number, that is "fundamentally fascinating in some way".[1] Constants emerge in numerous distinctive zones of science, with constants, for example, e and π happening in such various settings as geometry, number hypothesis and math.

What it implies for a consistent to emerge "commonly", and what makes a steady "intriguing", is eventually a matter of taste, and some scientific constants are outstanding more for recorded reasons than for their inherent numerical investment. The more mainstream constants have been considered all through the ages and figured to numerous decimal spots.

All scientific constants are quantifiable numbers and normally are likewise calculable numbers (Chaitin's steady being a huge special case).

Substance  [hide]

1 Common scientific constants

1.1 Archimedes' steady π

1.2 Euler's number e

1.3 Pythagoras' steady √2

1.4 The nonexistent unit i

2 Constants in developed science

2.1 The Feigenbaum constants α and δ

2.2 Apéry's steady ζ(3)

2.3 The brilliant degree φ

2.4 The Euler–mascheroni steady γ

2.5 Conway's steady λ

2.6 Khinchin's steady K

3 Mathematical interests and unspecified constants

3.1 Simple delegates of sets of numbers

3.2 Chaitin's steady Ω

3.3 Unspecified constants

3.3.1 In integrals

3.3.2 In differential mathematical statements

4 Notation

4.1 Representing constants

4.2 Symbolizing and naming of constants

5 Table of chose scientific constants

6 See likewise

7 Notes

8 Extern

Common mathematical constants

These are constants which one is liable to experience amid precollege instruction in numerous nations.

Archimedes' steady π[edit]

Fundamental article: Pi

The circuit of a round with measurement 1 is π.

The steady π (pi) has a characteristic definition in Euclidean geometry (the proportion between the boundary and width of a ring), yet might likewise be found in numerous better places in math: for instance the Gaussian fundamental in mind boggling examination, the foundations of solidarity in number hypothesis and Cauchy appropriations in likelihood. Then again, its comprehensiveness is not constrained to unadulterated arithmetic. Undoubtedly, different formulae in physical science, for example, Heisenberg's instability rule, and constants, for example, the cosmological steady incorporate the consistent π. The vicinity of π in physical standards, laws and formulae can have extremely straightforward clarifications. For instance, Coulomb's law, portraying the backwards square proportionality of the greatness of the electrostatic drive between two electric charges and their separation, states that, in SI units,

F = \frac{1}{4\pi\varepsilon_0}\frac{\left|q_1 q_2\right|}{r^2}.[2]

Other than {\varepsilon_0} relating to the dielectric steady in vacuum, the {4\pi r^2} consider in the above denominator communicates straightforwardly the surface of a circle with range r, having along these lines an extremely cement significance.

The numeric estimation of π is pretty nearly 3.14159. Retaining progressively exact digits of π is a world record interest.

Euler's number e[edit]

Exponential development (green) depicts numerous physical phenomena.

Euler's number e, otherwise called the exponential development steady, shows up in numerous ranges of science, and one conceivable meaning of it is the estimation of the accompanying interpretation:

e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n

Case in point, the Swiss mathematician Jacob Bernoulli found that e emerges in accumulating funds: A record that begins at $1, and yields enthusiasm at yearly rate R with persistent exacerbating, will gather to er dollars at the end of one year. The steady e additionally has applications to likelihood hypothesis, where it emerges in a manner not clearly identified with exponential development. Assume that a player plays an opening machine with an one in n likelihood of winning, and plays it n times. At that point, for substantial n, (for example, a million) the likelihood that the player will win nothing at all is (more or less) 1/e.

An alternate application of e, found to some extent by Jacob Bernoulli alongside French mathematician Pierre Raymond de Montmort, is in the issue of confusions, otherwise called the cap check problem.[3] Here n visitors are welcome to a gathering, and at the entryway every visitor checks his cap with the steward who then places them into marked boxes. Be that as it may the steward does not know the name of the visitors, thus must place them into boxes chose at irregular. The issue of de Montmort is: what is the likelihood that none of the caps gets put into the right box. The response is

p_n = 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\cdots+(-1)^n\frac{1}{n!}

also as n has a tendency to vastness, pn approaches 1/e.

The numeric estimation of e is roughly 2.71828.

Pythagoras' consistent √2[edit]

The square base of 2 is equivalent to the length of the hypotenuse of a right triangle with legs of length 1.

The square foundation of 2, frequently known as root 2, radical 2, or Pythagoras' steady, and composed as √2, is the positive mathematical number that, when increased without anyone else's input, gives the number 2. It is all the more decisively called the essential square base of 2, to recognize it from the negative number with the same property.

Geometrically the square foundation of 2 is the length of a slanting over a square with sides of one unit of length; this takes after from the Pythagorean hypothesis. It was most likely the first number known to be unreasonable. Its numerical worth truncated to 65 decimal spots is:

1.41421356237309504880168872420969807856967187537694807317667973799... (succession A002193 in OEIS).

The square foundation of 2.

The snappy estimate 99/70 (≈ 1.41429) for the square base of two is often utilized. Regardless of having a denominator of just 70, it varies from the right esteem by short of what 1/10,000 (approx. 7.2 × 10 −5).

The fanciful unit i[edit]

Primary article: Imaginary unit

i in the complex or cartesian plane. Genuine numbers lie on the even pivot, and fanciful numbers lie on the vertical hub

The fanciful unit or unit nonexistent number, signified as i, is a numerical idea which expands the genuine number framework ℝ to the complex number framework ℂ, which thusly gives no less than one root to each polynomial P(x) (see arithmetical conclusion and principal hypothesis of variable based math). The fanciful unit's center property is that i2 = −1. The expression "fanciful" is utilized on the grounds that there is no genuine number having a negative square.

There are indeed two complex square bases of −1, to be specific i and −i, exactly as there are two complex square foundations of each other genuine number, with the exception of zero, which has one twofold square root.

In connections where i is vague or tricky, j or the Greek ι (see elective documentations) is now and then utilized. In the controls of electrical designing and control frameworks building, the fanciful unit is regularly signified by j rather than i, in light of the fact that i is ordinarily used to mean electr

Constants in advanced mathematics

These are constants which are experienced oftentimes in higher math.

The Feigenbaum constants α and δ[edit]

Bifurcation chart of the logistic guide.

Emphasess of constant maps serve as the most straightforward cases of models for dynamical systems.[4] Named after scientific physicist Mitchell Feigenbaum, the two Feigenbaum constants show up in such iterative procedures: they are numerical invariants of logistic maps with quadratic greatest points[5] and their bifurcation charts.

The logistic guide is a polynomial mapping, regularly refered to as an original sample of how clamorous conduct can emerge from exceptionally basic non-straight dynamical comparisons. The guide was promoted in an original 1976 paper by the Australian scientist Robert May,[6] partially as a discrete-time demographic model undifferentiated from the logistic mathematical statement initially made by Pierre François Verhulst. The distinction mathematical statement is planned to catch the two impacts of proliferation and starvation.

The numeric estimation of α is more or less 2.5029. The numeric estimation of δ is pretty nearly 4.6692.

Apéry's steady ζ(3)[edit]

\zeta(3) = 1 + \frac{1}{2^3} + \frac{1}{3^3} + \frac{1}{4^3} + \cdots

Notwithstanding being an extraordinary estimation of the Riemann zeta capacity, Apéry's steady emerges regularly in various physical issues, incorporating in the second- and third-request terms of the electron's gyromagnetic degree, processed utilizing quantum electrodynamics.[7] The numeric estimation of ζ(3) is give or take 1.2020569.

The brilliant degree φ[edit]

Brilliant rectangles in an icosahedron

F\left(n\right)=\frac{\varphi^n-(1-\varphi)^n}{\sqrt 5}

An unequivocal equation for the nth Fibonacci number including the brilliant degree φ.

The number φ, likewise called the Golden degree, turns up as often as possible in geometry, especially in figures with pentagonal symmetry. In fact, the length of a consistent pentagon's askew is φ times its side. The vertices of a consistent icosahedron are those of three commonly orthogonal brilliant rectangles. Additionally, it shows up in the Fibonacci grouping, identified with development by recursion.[8] The brilliant degree has the slowest merging of any nonsensical number. It is, therefore, one of the most detrimental possibilities of Lagrange's close estimation hypothesis and it is an extremal instance of the Hurwitz disparity for Diophantine estimates. This may be the reason plot near the brilliant proportion frequently appear in phyllotaxis (the development of plants).[9] It is give or take equivalent to 1.61803398874, or, all the more exactly \scriptstyle\frac{1+\sqrt{5}}{2}.

The Euler–mascheroni steady γ[edit]

The territory between the two bends (red) keeps an eye on a farthest point.

The Euler–mascheroni steady is a repeating consistent in number hypothesis. The French mathematician Charles Jean de la Vallée-Poussin demonstrated in 1898 that when taking any positive number n and partitioning it by every positive whole number m short of what n, the normal portion by which the remainder n/m misses the mark regarding the following whole number has a tendency to \gamma as n has a tendency to interminability. Shockingly, this normal doesn't keep an eye on one half. The Euler–mascheroni steady likewise shows up in Merten's third hypothesis and has relations to the gamma work, the zeta capacity and numerous diverse integrals and arrangement. The meaning of the Euler–mascheroni consistent shows a nearby connection between the discrete and the nonstop (see bends on the left).

The numeric estimation of \gamma is pretty nearly 0.57721.

Conway's steady λ[edit]

\begin{matrix} 1 \\ 11 \\ 21 \\ 1211 \\ 111221 \\ 312211 \\ \vdots \end{matrix}

Conway's look-and-say arrangement

Conway's steady is the invariant development rate of all inferred strings like the look-and-say arrangement (aside from one insignificant one).[10]

It is given by the extraordinary positive genuine foundation of a polynomial of degree 71 with number coefficients.[10]

The estimation of λ is pretty nearly 1.30357.

Khinchin's steady K[edit]

On the off chance that a genuine number r is composed as a basic proceeded with part:

r=a_0+\dfrac{1}{a_1+\dfrac{1}{a_2+\dfrac{1}{a_3+\cdots}}},

where ak are common numbers for all k

at that point, as the Russian mathematician Aleksandr Khinchin demonstrated in 1934, the utmost as n has a tendency to endlessness of the geometric mean: (a1a2...an)1/n exists and is a steady, Khinchin's consistent, with the exception of a set of measure 0.[11][12]

The numeric estimation of K is pr

Mathematical curiosities and unspecified constants

Basic agents of sets of numbers[edit]

This Babylonian mud tablet gives a rough guess of the square establish of 2 in four sexagesimal figures: 1; 24, 51, 10, which is precise to around six decimal figures.[13]

c=\sum_{j=1}^\infty 10^{-j!}=0.\underbrace{\overbrace{110001}^{3!\text{ digits}}000000000000000001}_{4!\text{ digits}}000\dots\,

Liouville's steady is a straightforward case of a transcendental number.

A few constants, for example, the square base of 2, Liouville's consistent and Champernowne steady:

C_{10} = 0.{\color{blue}{1}}2{\color{blue}{3}}4{\color{blue}{5}}6{\color{blue}{7}}8{\color{blue}{9}}10{\color{blue}{11}}12{\color{blue}{13}}14{\color{blue}{15}}16\dots

are not imperative numerical invariants yet hold enthusiasm being straightforward agents of exceptional sets of numbers, the nonsensical numbers,[14] the transcendental numbers[15] and the typical numbers (in base 10)[16] separately. The revelation of the unreasonable numbers is normally ascribed to the Pythagorean Hippasus of Metapontum who demonstrated, in all probability geometrically, the silliness of the square foundation of 2. With respect to Liouville's consistent, named after French mathematician Joseph Liouville, it was the first number to be demonstrated transcendental.[17]

Chaitin's steady Ω[edit]

In the software engineering subfield of algorithmic data hypothesis, Chaitin's consistent is the true number speaking to the likelihood that an arbitrarily picked Turing machine will end, framed from a development because of Argentine-American mathematician and workstation researcher Gregory Chaitin. Chaitin's consistent, however not being processable, has been turned out to be transcendental and ordinary. Chaitin's consistent is not widespread, depending intensely on the numerical encoding utilized for Turing machines; be that as it may, its fascinating properties are free of the encoding.

Unspecified constants[edit]

At the point when unspecified, constants show classes of comparable articles, generally works, all equivalent up to a steady actually talking, this is may be seen as 'likeness up to a consistent'. Such constants show up much of the time when managing integrals and differential mathematical statements. Despite the fact that unspecified, they have a particular worth, which regularly is not critical.

Results with diverse constants of mix of y'(x)=-2y+e^{-x}\,.

In integrals[edit]

Inconclusive integrals are called uncertain in light of the fact that their answers are just exceptional up to a steady. Case in point, when working over the field of genuine numbers

\int\cos x\ dx=\sin x+c

where C, the steady of mix, is a subjective settled true number.[18] as it were, whatever the estimation of C, separating sin x + C concerning x dependably yields cos x.

In differential equations[edit]

In a comparable manner, constants show up in the answers for differential comparisons where insufficient starting qualities or limit conditions are given. Case in point, the conventional differential mathematical statement y' = y(x) has result Cex where C is a subjective consistent.

At the point when managing fractional differential mathematical statements, the constants may be capacities, consistent concerning a few variables (yet not so much every one of them). For instance, the PDE

\frac{\partial f(x,y)}{\partial x}=0

has results f(x,y) = C(y), where C(y) is a self-assertive capacity in the variable y

Notation

Speaking to constants[edit]

It is regular to express the numerical estimation of a consistent by providing for its decimal representation (or simply the initial couple of digits of it). For two reasons this representation may cause issues. Initially, despite the fact that judicious numbers all have a limited or regularly rehashing decimal extension, unreasonable numbers don't have such a representation making them difficult to totally portray in this way. Additionally, the decimal extension of a number is not so much exceptional. Case in point, the two representations 0.999... furthermore 1 are equivalent[19][20] as in they speak to the same number.

Computing digits of the decimal extension of constants has been a typical venture for a long time. Case in point, German mathematician Ludolph van Ceulen of the sixteenth century used a real piece of his life computing the initial 35 digits of pi.[21] Using workstations and supercomputers, a portion of the scientific constants, including π, e, and the square base of 2, have been registered to more than one hundred billion digits. Quick calculations have been produced, some of which — with respect to Apéry's steady — are surprisingly quick.

G=\left . \begin{matrix} 3 \underbrace{ \uparrow \ldots \uparrow } 3 \\ \underbrace{\vdots } \\ 3 \uparrow\uparrow\uparrow\uparrow 3 \end{matrix} \right \} \text{64 layers}

Graham's number characterized utilizing Knuth's up-shaft documentation.

A few constants vary such a great amount from the normal kind that another documentation has been imagined to speak to them sensibly. Graham's number shows this as Knuth's up-shaft documentation is used.[22][23]

It may be of enthusiasm to speak to them utilizing proceeded with parts to perform different studies, including measurable examination. Numerous numerical constants have a diagnostic structure, that is they could be built utilizing great known operations that loan themselves promptly to count. Not all constants have known explanatory structures, however; Grossman's constant[24] and Foias' constant[25] are cases.

Symbolizing and naming of constants[edit]

Symbolizing constants with letters is a regular method for making the documentation more brief. A standard gathering, prompted by Leonhard Euler in the eighteenth century, is to utilize lower case letters from the earliest starting point of the Latin letter set a,b,c,\dots\, or the Greek letter set \alpha,\beta,\,\gamma,\dots\, when managing constants as a rule.

Erdős–borwein consistent E_b\,

Embree–trefethen consistent \beta*\,

Brun's consistent for twin prime B_2\,

Champernowne constants C_b

cardinal number aleph nothing \aleph_0

Cases of various types of documentation for constants.

Be that as it may, for more critical constants, the images may be more mind boggling and have an additional letter, a mark, a number, a lemniscate or use distinctive letters in order, for example, Hebrew, Cyrillic or Gothic.[23]

\mathrm{googol}=10^{100}\,\ ,\ \mathrm{googolplex}=10^\mathrm{googol}=10^{10^{100}}\,

Some of the time, the image speaking to a consistent is an entire word. For instance, American mathematician Edward Kasner's 9-year-old nephew authored the names googol and googolplex.[23][26]

The general allegorical steady is the proportion, for any parabola, of the bend length of the illustrative portion (red) framed by the latus rectum (blue) to the central parameter (green).

The names are either identified with the significance of the steady (all inclusive explanatory consistent, twin prime consistent, ...) or to a particular individual (Sierpiński's consistent, Josephson

Table of selected mathematical constants

Fundamental article: List of numerical constants

Truncations utilized:

R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)

Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation

Symbol value name field n first described # of known digits

0

= 0 zero gen r c. 7th–5th century Bc n/A

1

= 1 one, Unity gen r n/A

i

= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A

π

≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]

e

≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000

√2

≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444

√3

≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC

√5

≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC

\gamma

≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771

\phi

≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000

\rho

≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928

\beta*

≈ 0.70258 embree–trefethen constant nut

\delta

≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975

\alpha

≈ 2.50290 78750 95892 82228 39028 73218 21578 feigenbaum constant cht

C2

≈ 0.66016 18158 46869 57392 78121 10014 55577 twin prime constant nut 5,020

M1

≈ 0.26149 72128 47642 78375 54268 38608 69585 meissel–mertens constant nut 1866

1874 8,010

B2

≈ 1.90216 05823 brun's consistent for twin primes nut 1919 10

B4

≈ 0.87058 83800 brun's consistent for prime quadruplets nut

\lambda

≥ –2.7 • 10−9 de Bruijn–newman constant nut 1950? none

K

≈ 0.91596 55941 77219 01505 46035 14932 38411 catalan's constant com 15,510,000,000

K

≈ 0.76422 36535 89220 66299 06987 31250 09232 landau–ramanujan constant nut 30,010

K

≈ 1.13198 824 viswanath's constant nut 8

B'l

= 1 legendre's constant nut r n/A

\mu

≈ 1.45136 92348 83381 05028 39684 85892 02744 ramanujan–soldner constant nut 75,500

EB

≈ 1.60669 51524 15291 76378 33015 23190 92458 erdős–borwein constant nut i

\beta

≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana

\lambda

≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385

\sigma

≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993

\lambda, \mu

≈ 0.62432 99885 43550 87099 29363 83100 83724 golomb–dickman constant com, Nut 1930

1964

≈ 0.64341 05463 cahen's constant t 1891 4000

≈ 0.66274 34193 49181 58097 47420 97109 25290 laplace utmost

≈ 0.80939 40205 alladi–grinstead constant[29] nut

\lambda

≈ 1.09868 58055 lengyel's constant[30] com 1992

≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut

\zeta (3)

≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000

\theta

≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850

≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]

≈ 1.46707 80794 porter's constant[32] nut 1975

≈ 1.53960 07178 lieb's square ice constant[33] com 1967

≈ 1.70521 11401 05367 76428 85514 53434 50816 niven's constant nut 1969

K

≈ 2.58498 17595 79253 21706 58935 87383 17116 sierpiński's consistent

≈ 2.68545 20010 65306 44530 97148 35481 79569 khinchin's constant nut 1934 7350

F

≈ 2.80777 02420 28519 36522 15011 86557 77293 fransén–robinson constant ana

L

≈ 0.5 landau's constant ana 1

P2

≈ 2.29558 71493 92638 07403 42980 49189 49039 universal illustrative constant gen t

Ω

≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t

C_{{}_{mrb}}
Fundamental article: List of numerical constants

Truncations utilized:

R – Rational number, I – Irrational number (may be logarithmic or transcendental), A – Algebraic number (unreasonable), T – Transcendental number (silly)

Gen – General, Nut – Number hypothesis, Cht – Chaos hypothesis, Com – Combinatorics, Inf – Information hypothesis, Ana – Mathematical investigation

Symbol value name field n first described # of known digits

0

= 0 zero gen r c. 7th–5th century Bc n/A

1

= 1 one, Unity gen r n/A

i

= √–1 imaginary unit, unit nonexistent number gen, Ana a 16th century n/A

π

≈ 3.14159 26535 89793 23846 26433 83279 50288 pi, Archimedes' steady or Ludolph's number gen, Ana t by c. 2000 Bc 10,000,000,000,000[27]

e

≈ 2.71828 18284 59045 23536 02874 71352 66249 e, Napier's steady, or Euler's number gen, Ana t 1618 100,000,000,000

√2

≈ 1.41421 35623 73095 04880 16887 24209 69807 pythagoras' steady, square base of 2 gen a by c. 800 Bc 137,438,953,444

√3

≈ 1.73205 08075 68877 29352 74463 41505 87236 theodorus' steady, square base of 3 gen a by c. 800 BC

√5

≈ 2.23606 79774 99789 69640 91736 68731 27623 square foundation of 5 gen a by c. 800 BC

\gamma

≈ 0.57721 56649 01532 86060 65120 90082 40243 euler–mascheroni constant gen, Nut 1735 14,922,244,771

\phi

≈ 1.61803 39887 49894 84820 45868 34365 63811 golden ratio gen a by third century Bc 100,000,000,000

\rho

≈ 1.32471 79572 44746 02596 09088 54478 09734 plastic constant nut a 1928

\beta*

≈ 0.70258 embree–trefethen constant nut

\delta

≈ 4.66920 16091 02990 67185 32038 20466 20161 feigenbaum constant cht 1975

\alpha

≈ 2.50290 78750 95892 82228 39028 73218 21578 feigenbaum constant cht

C2

≈ 0.66016 18158 46869 57392 78121 10014 55577 twin prime constant nut 5,020

M1

≈ 0.26149 72128 47642 78375 54268 38608 69585 meissel–mertens constant nut 1866

1874 8,010

B2

≈ 1.90216 05823 brun's consistent for twin primes nut 1919 10

B4

≈ 0.87058 83800 brun's consistent for prime quadruplets nut

\lambda

≥ –2.7 • 10−9 de Bruijn–newman constant nut 1950? none

K

≈ 0.91596 55941 77219 01505 46035 14932 38411 catalan's constant com 15,510,000,000

K

≈ 0.76422 36535 89220 66299 06987 31250 09232 landau–ramanujan constant nut 30,010

K

≈ 1.13198 824 viswanath's constant nut 8

B'l

= 1 legendre's constant nut r n/A

\mu

≈ 1.45136 92348 83381 05028 39684 85892 02744 ramanujan–soldner constant nut 75,500

EB

≈ 1.60669 51524 15291 76378 33015 23190 92458 erdős–borwein constant nut i

\beta

≈ 0.28016 94990 23869 13303 bernstein's constant[28] ana

\lambda

≈ 0.30366 30028 98732 65859 74481 21901 55623 gauss–kuzmin–wirsing constant com 1974 385

\sigma

≈ 0.35323 63718 54995 98454 hafner–sarnak–mccurley constant nut 1993

\lambda, \mu

≈ 0.62432 99885 43550 87099 29363 83100 83724 golomb–dickman constant com, Nut 1930

1964

≈ 0.64341 05463 cahen's constant t 1891 4000

≈ 0.66274 34193 49181 58097 47420 97109 25290 laplace utmost

≈ 0.80939 40205 alladi–grinstead constant[29] nut

\lambda

≈ 1.09868 58055 lengyel's constant[30] com 1992

≈ 3.27582 29187 21811 15978 76818 82453 84386 lévy's constant nut

\zeta (3)

≈ 1.20205 69031 59594 28539 97381 61511 44999 apéry's constant i 1979 15,510,000,000

\theta

≈ 1.30637 78838 63080 69046 86144 92602 60571 mills' constant nut 1947 6850

≈ 1.45607 49485 82689 67139 95953 51116 54356 backhouse's constant[31]

≈ 1.46707 80794 porter's constant[32] nut 1975

≈ 1.53960 07178 lieb's square ice constant[33] com 1967

≈ 1.70521 11401 05367 76428 85514 53434 50816 niven's constant nut 1969

K

≈ 2.58498 17595 79253 21706 58935 87383 17116 sierpiński's consistent

≈ 2.68545 20010 65306 44530 97148 35481 79569 khinchin's constant nut 1934 7350

F

≈ 2.80777 02420 28519 36522 15011 86557 77293 fransén–robinson constant ana

L

≈ 0.5 landau's constant ana 1

P2

≈ 2.29558 71493 92638 07403 42980 49189 49039 universal illustrative constant gen t

Ω

≈ 0.56714 32904 09783 87299 99686 62210 35555 omega constant ana t

C_{{}_{mrb}}