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...

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

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

Ankeny–Artin–Chowla theorem (number theory) Anne's theorem (geometry) Apéry's theorem (number theory) Apollonius's theorem (plane geometry) Appell–Humbert theorem (complex...

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...

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...

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...

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...

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:...

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

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...

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...

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

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...

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

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

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

, 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...

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...

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)...

{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....

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 However...

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

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...

region in three-dimensional Euclidean space by the generalized Jordan curve theorem. The outward-pointing unit normal vector field would then give an orientation...

{\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...

Anthemius of Tralles Leonidas Alaoglu (1914–1981) - Known for Banach- Alaoglu theorem. Charalambos D. Aliprantis (1946–2009) - Founder and Editor-in-Chief of...

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

runs 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...