LMATH_CONSTANTS_EXTENTED (TagTable / global constants)


Constant identifier, values and description

Identifier & ValueDescription
LMATH_ALLADI_GRINSTEAD
0.8093940205
Alladi-Grinstead constant is the Infinite product constant
LMATH_APERY
1.20205690315959428539973816151145
Apery's constant
LMATH_BACKHOUSE
1.45607494858268967139959535111654
Backhouse's constant
LMATH_BERNSTEIN
0.28016949902386913303
Bernstein's constant
LMATH_BRAUN_PRIME_QUADR
0.8705883800
Braun's constant for prime quadruplets
LMATH_BRAUN_TWIN_PRIME
1.9021605823
Braun's constant for twin primes
LMATH_BRUIJN_NEWMAN
-2.7E-9
de Bruijn-Newman constant
LMATH_CAHEN
0.6434105463
Cahen's constant is defined as an infinite series of unit fractions, with alternating signs, derived from Sylvester's sequence
LMATH_CATALAN
0.91596559417721901505460351493238
Catalan's constant G, which appears in combinatorics
LMATH_EMBREE_TREFETHEN
0.70258
Embree-Trefethen constant is a threshold value labelled β*
LMATH_ERDOS_BORWEIN
1.60669515241529176378330152319092
Erdos-Borwein constant is the sum of the reciprocals of the Mersenne numbers
LMATH_EULER_MASCHERONI
0.57721566490153286060651209008240
Euler-Mascheroni constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ).
LMATH_EULER_MASCHERONI_INV
1.73245471460063347358302531586084
Euler-Mascheroni inverse constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ).
LMATH_EULER_MASCHERONI_SQR
0.33317792380771867431837613635524
Euler-Mascheroni square constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ).
LMATH_FEIGENBAUM_ALFA
2.50290787509589282228390287321822
Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map
LMATH_FEIGENBAUM_DELTA
4.66920160910299067185320382046620
Feigenbaum constants are two mathematical constants which both express ratios in a bifurcation diagram for a non-linear map
LMATH_FRANSEN_ROBINSON
2.80777024202851936522150118655777
Fransén-Robinson constant, sometimes denoted F, is the mathematical constant that represents the area between the graph of the reciprocal Gamma function, 1 / Γ(x), and the positive x axis
LMATH_GAUSS_KUZMIN_WIRSING
0.30366300289873265859744812190156
Gauss-Kuzmin-Wirsing constant is the transfer operator of the Gauss map
LMATH_GOLOMB_DICKMAN
0.62432998854355087099293638310083
Golomb-Dickman constant arises in the theory of random permutations and in number theory
LMATH_GOMPERTZ
0.59634736232319407434107849936928
Gompertz Constant OEIS A073003
LMATH_HAFNER_SARNAK_MCCURLEY
0.35323637185499598454
Hafner-Sarnak-McCurley constant representing the probability that the determinants of two randomly chosen square integer matrices will be relatively prime
LMATH_KHINCHIN
2.68545200106530644530971483548180
Khinchin's constant for almost all real numbers x, coefficients ai of the continued fraction expansion of x have a finite geometric mean that is independent of the value of x and is known as Khinchin's constant
LMATH_LANDAU
0.5
Landau's constant
LMATH_LANDAU_RAMANUJAN
0.76422365358922066299069873125009
Landau-Ramanujan constant
LMATH_LAPLACE_LIMIT
0.66274341934918158097474209710925
Laplace limit is the maximum value of the eccentricity for which a solution to Kepler's equation, in terms of a power series in the eccentricity, converges
LMATH_LEGENDRE
1.0
Legendre's constant, capture the asymptotic behavior of the prime-counting function pi(x). Its value is now known to be exactly 1.
LMATH_LENGYEL
1.0986858055
Lengyel's constant
LMATH_LEVY
3.27582291872181115978768188245384
Levy's constant occurs in an expression for the asymptotic behavior of the denominators of the convergent of continued fractions
LMATH_LIEB_QUARE_ICE
1.5396007178
Lieb's square ice constant is a mathematical constant used in the field of combinatorics to quantify the number of Eulerian orientations of grid graphs.
LMATH_MEISSEL_MERTEENS
0.26149721284764278375542683860870
Meissel–Mertens constant limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm
LMATH_MILLS
1.30637788386308069046861449260261
Mills' constant is defined as the smallest positive real number A such that the floor function of the double exponential function [A^{3^{n}}] is a prime number, for all natural numbers n.
LMATH_MRB
0.187859
MRB constant is defined as the upper limit of the partial sums
LMATH_NIVEN
1.70521114010536776428855145343451
Niven's constant is the largest exponent appearing in the prime factorization of any natural number n "on average"
LMATH_OMEGA
0.56714329040978387299996866221036
Omega constant defined as the unique real number that satisfies the equation - Omega e^Omega = 1
LMATH_PARABOLIC
2.29558714939263807403429804918949
Universal parabolic constant is defined as the ratio, for any parabola, of the arc length of the parabolic segment formed by the latus rectum to the focal parameter.
LMATH_PLASTIC_RATIO
1.32471795724474602596090885447810
Plastic number the unique real solution of the cubic equation x^3=x+1
LMATH_PORTER
1.4670780794
Porter's constant C arises in the study of the efficiency of the Euclidean algorithm
LMATH_RAMANUJAN_SOLDNER
1.45136923488338105028396848589203
Ramanujan-Soldner constant defined as the unique positive zero of the logarithmic integral function
LMATH_SIERPINSKI
2.58498175957925321706589358738317
Sierpiński's constant usually denoted as K.
LMATH_TWIN_PRIME
0.66016181584686957392781211001456
twin prime constant C2
LMATH_VISWANATH
1.1319882487943
Viswanath's constant, the growth rate of the random Fibonacci sequence is equal to