A002117 in the OEIS). It is named after Roger Apéry, who proved that it is an irrational number. Apéry's constant arises naturally in a number of physical...

mathematician Roger Apéry in 1979. It is however not known whether it is algebraic or transcendental. The numeric value of Apéry's constant is approximately:...

In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ(3) is irrational. That is, the number ζ ( 3 ) = ∑ n =...

constants named after people. Eponymous constants and their influence on scientific citations have been discussed in the literature. Apéry's constant...

Roger Apéry (French: [apeʁi]; 14 November 1916, Rouen – 18 December 1994, Caen) was a Greek-French mathematician most remembered for Apéry's theorem, which...

Constant". MathWorld. Weisstein, Eric W. "Omega Constant". MathWorld. Weisstein, Eric W. "Apéry's Constant". MathWorld. Weisstein, Eric W. "Laplace Limit"...

and ln(3) The Euler-Mascheroni constant γ Apéry's constant ζ(3) The Feigenbaum constants δ and α Khinchin's constant Among the numbers x whose continued...

to ζ(3)/D, where ζ is the Riemann zeta function and ζ(3) ≈ 1.202 is Apéry's constant. For instance, for edge weights that are uniformly distributed on the...

Euler's constant γ {\displaystyle \gamma } and Catalan's constant G {\displaystyle G} irrational? Are they transcendental? Is Apéry's constant ζ ( 3 )...

Catalan constant were constructed by E. Karatsuba. Using these series, calculating Catalan's constant is now about as fast as calculating Apéry's constant, ζ...

{1}{2^{3}}}+{\frac {1}{3^{3}}}+\cdots =1.202056903159594285399...} is Apéry's constant. Taking the limit s → + ∞ {\displaystyle s\rightarrow +\infty } through...

sum of the reciprocals of the cubes of positive integers is called Apéry's constant ζ(3) , and equals approximately 1.2021 . This number is irrational...

\varphi ,} the Riemann zeta function ζ , {\displaystyle \zeta ,} and Apéry's constant ζ ( 3 ) . {\displaystyle \zeta (3).} As no two Ford circles intersect...

{1}{2}}+{\frac {1}{3}}+\cdots =\infty \!} The value ζ(3) is also known as Apéry's constant and has a role in the electron's gyromagnetic ratio. The value ζ(3)...

1} . By contrast, the properties of the odd-indexed zeta constants, including Apéry's constant ζ ( 3 ) {\displaystyle \zeta (3)} , are almost completely...

{\displaystyle \int _{0}^{a}H_{x,3}\,dx=aA-{\frac {1}{2}}H_{a,2},} where A is Apéry's constant ζ(3), and ∑ k = 1 n H k , m = ( n + 1 ) H n , m − H n , m − 1  for ...

numbers such as Apéry's constant or the Euler–Mascheroni constant. Another extremely difficult unsolved problem is the so-called constant or identity problem...

constant, π 3 {\displaystyle \pi ^{3}} , π 4 {\displaystyle \pi ^{4}} , Apéry's constant ζ ( 3 ) {\displaystyle \zeta (3)} , ζ ( 5 ) {\displaystyle \zeta (5)}...

odd positive integers n ≥ 3 {\displaystyle n\geq 3} ; in particular Apéry's constant ζ(3), which is known to be irrational. For the other numbers ζ(5),...

Mathematical Constants (Encyclopedia of Mathematics and its Applications, Series Number 94), Cambridge University Press, pp. 130–133, ISBN 0521818052 Apéry, Roger...

as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant. At the current CBR...

as the Boltzmann constant, ħ as the Planck constant divided by 2π and c as the speed of light in vacuum, and ζ(3) as Apéry's constant. At the current CBR...

zeta function (more specifically is ζ ( 3 ) {\displaystyle \zeta (3)} Apéry's constant). Frieze and Steele also proved convergence in probability. Svante...

Some of the constants used in science are named after great scientists. By this convention, their names are immortalised. Below is the list of the scientists...

, the solution to the Basel problem, Apéry's constant ζ ( 3 ) {\displaystyle \zeta (3)} , proved by Roger Apéry to be an irrational number, and the "critical...

{1}{9}}+{\frac {1}{16}}+\cdots ={\frac {\pi ^{2}}{6}}.} Similarly, Apéry's constant is an irrational number, the sum of the cubed unit fractions. The binary...

integrals of mathematical physics and such classical constants as Euler's, Catalan's and Apéry's constants. An additional advantage of the method FEE is the...

y-cruncher is a computer program for the calculation of some mathematical constant with theoretical accuracy limited only by computing time and available...

includes, alongside the algebraic numbers, many well known mathematical constants such as the number π. Sums and products of periods remain periods, such...

over all primes, ζ(s) denotes the Riemann zeta function, and ζ(3) is Apéry's constant. (sequence A082695 in the OEIS) More generally, the sum of the reciprocals...