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Use the definition of the q-series (a;q)_n=product_(j=0)^(n-1)(1-aq^j) (1) and define [N; M]=((q^(N-M+1);q)_M)/((q;q)_m). (2) Then P. Borwein has conjectured that (1) the ...

The Borwein integrals are the class of definite integrals defined by I_n=1/piint_0^inftyx^(-(n+1)/2)product_(k=1,3,...)^nsin(x/k)dx for odd n. The integrals are curious ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

A bra <psi| is a vector living in a dual vector space to that containing kets |psi>. Bras and kets are commonly encountered in quantum mechanics. Bras and kets can be ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...

The term "bundle" is an abbreviated form of the full term fiber bundle. Depending on context, it may mean one of the special cases of fiber bundles, such as a vector bundle ...

Given a group G, the algebra CG is a vector space CG={suma_ig_i|a_i in C,g_i in G} of finite sums of elements of G, with multiplication defined by g·h=gh, the group ...

The word canonical is used to indicate a particular choice from of a number of possible conventions. This convention allows a mathematical object or class of objects to be ...

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

"Casting out nines" is an elementary check of a multiplication which makes use of the congruence 10^n=1 (mod 9). Let decimal numbers be written a=a_n...a_2a_1a_0, ...