apery

The Apery set of a [not equal to] 0 in S is defined as Ap(S, a) = {x [member of] S|x - a [not member of] S}.

There is a vast literature in number theory analysing the modular congruences of famous sequences (Pascal triangle, Fibonacci, Catalan, Motzkin, Apery numbers, see Deutsch and Sagan (2006); Xin and Xu (2011); Rowland and Zeilberger (2014); Kauers et al.

If S is a numerical semigroup and m [member of] S \ {0}, then the Apery set of m in S (see [9]) is Ap(S, m) = {s [member of] S | s - m [not member of] S}.

It was shown theoretically that for long signum-chirps with [f.sub.0] = 0, we have [[delta].sub.E] = 7[zeta](3)/[[pi].sup.2], where [zeta] denotes the Riemann zeta function, and [zeta](3) [congruent to] 1.202 is known as the Apery's constant.

Apery, a French mathematician, proved that the number [zeta](3) is irrational.

Then there are Apery's savory puffs filled with ham, sesame seeds and cheese.

In this ploy he re-enacted the roles of two of Apes's main characters and surreptitiously confirmed the contradictions of "Apery" that the novel unmasks.

Francois Apery of the University of Upper Alsace in Mulhouse, France, has now captured the essence of the process, known as sphere eversion, in a surprisingly simple model.

Leshchiner [12] proved accelerated series for the values [beta](2n + 1) in the spirit of Apery's series (1).

French mathematician Francois Apery, a student of topologist Bernard Morin at the University of Strasbourg, finally worked out the equations in 1984.