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 = 1...

Is Apéry's constant transcendental? More unsolved problems in mathematics ζ(3) was named Apéry's constant after the French mathematician Roger Apéry, who...

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

Albert–Brauer–Hasse–Noether theorem (algebras) Ankeny–Artin–Chowla theorem (number theory) Apéry's theorem (number theory) Artin–Verdier duality theorem (number theory)...

is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics...

the Radboud University Nijmegen, the Netherlands. He has reproved Apéry's theorem that ζ(3) is irrational, and expanded it. Zudilin proved that at least...

of Grothendieck's period conjecture for mixed Tate motives. Apéry's constant Apéry's theorem Particular values of the Riemann zeta function Wadim Zudilin...

These and additional values are: It is known that ζ(3) is irrational (Apéry's theorem) and that infinitely many of the numbers ζ(2n + 1) : n ∈ N {\displaystyle...

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:...

The 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...

]^{4}\}} Lemniscatic example for the fifth power theorem: A next example for the fifth power theorem: If two positive numbers a {\displaystyle a} and...

University of California, Santa Barbara in fall 2015. Roger Apéry proved Apéry's theorem at the age of 63. Musical ability is inherent in almost all people...

expository writings, among them a paper on Apéry's theorem on the irrationality of ζ(3) and his book on Fermat's Last Theorem. Van der Poorten received the Australian...

irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the...

by Frits Beukers in his 1978 paper giving an alternative proof of Apéry's theorem. He proved the formula when s = 0, and proved an equivalent formulation...

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

Catalan's constant G {\displaystyle G} irrational? Are they transcendental? Is Apéry's constant ζ ( 3 ) {\displaystyle \zeta (3)} transcendental? Which transcendental...

Natural logarithms, e.g. ln(2) and ln(3) The Euler-Mascheroni constant γ Apéry's constant ζ(3) The Feigenbaum constants δ and α Khinchin's constant Among...

at 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)...

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

coefficients), in both qualitative and quantitative ways. The fundamental theorem of algebra tells us that if we have a non-constant polynomial with rational...

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

{\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...

, 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...

progrès récents sur la géométrie arithmétique des surfaces Nicolas Rougerie Théorèmes de de Finetti, limites de champ moyen et condensation de Bose–Einstein...

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

{1}{4}}+{\frac {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....

attempting to find the values at the positive odd integers (including Apéry's constant) as well, a problem that remains elusive today. The eta function...

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

numbers, are not known with high precision. The constant in the Berry–Esseen Theorem: 0.4097 < C < 0.4748 De Bruijn–Newman constant: 0 ≤ Λ ≤ 0.2 Chaitin's constants...