- In mathematics,
Apéry's constant is the sum of the
reciprocals of the
positive cubes. That is, it is
defined as the
number ζ(3)=∑n=1∞1n3=limn→∞(113+123+⋯+1n3)...
- 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∞1n3=113+123+133+⋯=1...
-
Roger Apéry (French: [apeʁi]; 14
November 1916,
Rouen – 18
December 1994, Caen) was a
French mathematician most
remembered for
Apéry's theorem,
which states...
-
fundamental way of the
solving process. An
extreme example is
Apery's theorem:
Roger Apery provided only the
ideas for a proof, and the
formal proof was...
-
salutis meae: et
exsultabit lingua mea
justitiam tuam. Domine,
labia mea
aperies: et os meum
annuntiabit laudem tuam.
Quoniam si
voluisses sacrificium,...
- The
verse Domine,
labia mea
aperies et os meum
annuntiabit laudem tuam is sung at the
opening of the
first canonical hour of the day...
-
approximately 2.5029. The
numeric value of δ is
approximately 4.6692.
Apery's constant is the sum of the
series ζ(3)=1+123+133+143+⋯{\displaystyle \zeta...
- it is also a
magic number for the
diamond cubic. It is also the
fourth Apéry number a3{\displaystyle a_{3}}
following 19,
where an=∑k=0n(nk)2(n+kk),{\displaystyle...
- Γ(12)=π;{\displaystyle \Gamma ({\tfrac {1}{2}})={\sqrt {\pi }};}
while inside Apéry's constant,
which represents the sum of the
reciprocals of all
positive cubes...
- Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A005259 (
Apery (
Apéry) numbers: Sum_0^n (binomial(n,k)*binomial(n+k,k))^2)". The On-Line Encyclopedia...