index of important irrational constants

index of important irrational constants

The following table lists some of the most important

irrational

constants in mathematics.

Of course importance is sometimes debatable. Hardly anyone disputes the importance of

π

or

e

(in fact, these are the only two constants in the OEIS to have the keyword “core” attached to them), but for other constants it is not quite clear cut. In general, if a given constant has a name (especially a name hyphenating two famous mathematicians’ last names) I consider it important.

Irrationality is not always clear cut either, e.g., it might be a mistake to exclude the

Euler-Mascheroni constant

γ

from this list.

The constants are given to 20

decimal places

.

0.1149420448532962007

Kepler-Bouwkamp constant

or polygon-inscribing constant

0.1234567891011121314

Champernowne’s constant

C

10

0.2078795763507619085

i

i

(has no

imaginary part

) or

e

-

π

2

0.2357111317192329313

http://planetmath.org/CopelandErdsConstant

Copeland-Erdős constant

0.2614972128476427837

Meissel-Mertens constant

0.3275822918721811159

Lévy’s constant

0.4146825098511116602

The

prime constant

ρ

0.5926327182016361971

Lehmer’s constant

0.6079271018540266286

6

π

2

, the probability that a random

integer

is

squarefree

0.6434105462883380261

Cahen’s constant

0.7642236535892206629

Landau-Ramanujan constant

0.8346268416740731862

Gauss’s constant

0.8862269254527580136

Γ

⁢

(

3

2

)

=

1

2

⁢

π

0.9159655941772190150

Catalan’s constant

K

1.2020569031595942853

Apéry’s constant

ζ

⁢

(

3

)

1.2254167024651776451

Γ

⁢

(

3

4

)

1.3063778838630806904

Mills’ constant

1.3247179572447460260

The

plastic constant

1.4142135623730950488

Square root

of two

2

1.4513692348833810502

Ramanujan-Soldner constant

1.6066951524152917637

Erdős-Borwein constant

1.6180339887498948482

The

golden ratio

ϕ

1.6449340668482264364

ζ

⁢

(

2

)

=

π

2

6

, the solution to the

Basel problem

1.7320508075688772935

Square root of three

3

1.7579327566180045327

Vijayaraghavan’s infinite

nested radical

1

+

2

+

3

+

4

+

5

+

…

1.7724538509055160273

Γ

⁢

(

1

2

)

=

π

2.2360679774997896964

Square root of five

5

2.6651441426902251887

2

2

2.6854520010653064453

Khinchin’s constant

2.4142135623730950488

The

silver ratio

δ

S

2.5849817595792532170

Sierpiński’s constant

2.7182818284590452354

The

natural log base

e

3.1415926535897932385

The ratio of a circle’s radius to its

circumference

π

3.6256099082219083119

Γ

⁢

(

1

4

)

4.1327313541224929385

2

⁢

e

⁢

π

4.6692116609102990671

Feigenbaum’s constant

δ

7.3890560989306502272

e

2

14.1347251417346937904

The imaginary part of the first nontrivial zero of the

Riemann zeta function

(the real part is

1

2

)

15.1542622414792641898

e

e

36.4621596072079117710

π

π

In looking these up in the OEIS, you can simply type them with a

decimal point

and no commas between the digits. If you get no results, try chopping off a couple of the least significant digits.

References

1

Alan Jeffrey,

Handbook of Mathematical Formulas and

Integrals

, 3rd Edition. New York: Elsevier Academic Press (2004): 223,

Section

11.1.4 Special values of

Γ

⁢

(

x

)

Title

index of important irrational constants

Canonical

name

IndexOfImportantIrrationalConstants

Date of creation

2013-03-22 17:03:10

Last modified on

2013-03-22 17:03:10

Owner

PrimeFan (13766)

Last modified by

PrimeFan (13766)

Numerical id

17

Author

PrimeFan (13766)

Entry type

Topic

Classification

msc 00A08

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