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The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

The number of ways a set of n elements can be partitioned into nonempty subsets is called a Bell number and is denoted B_n (not to be confused with the Bernoulli number, ...

Consecutive number sequences are sequences constructed by concatenating numbers of a given type. Many of these sequences were considered by Smarandache and so are sometimes ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

Given a homogeneous linear second-order ordinary differential equation, y^('')+P(x)y^'+Q(x)y=0, (1) call the two linearly independent solutions y_1(x) and y_2(x). Then ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

A quasigroup with an identity element e such that xe=x and ex=x for any x in the quasigroup. All groups are loops. In general, loops are considered to have very little in the ...

A magic square for which the number of letters in the word for each number generates another magic square. This definition depends, of course, on the language being used. In ...

Dickson (1913, 2005) defined an amicable triple to be a triple of three numbers (l,m,n) such that s(l) = m+n (1) s(m) = l+n (2) s(n) = l+m, (3) where s(n) is the restricted ...

If A is a normed algebra, a net {e_i} in A is called an approximate identity for A if sup_(i)|e_i|<infty and if for each a in A, e_ia->a and ae_i->a. Though this definition ...