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product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

A perfect power is a number n of the form m^k, where m>1 is a positive integer and k>=2. If the prime factorization of n is n=p_1^(a_1)p_2^(a_2)...p_k^(a_k), then n is a ...

A pi-prime is a prime number appearing in the decimal expansion of pi. The known examples are 3, 31, 314159, 31415926535897932384626433832795028841, ... (OEIS A005042). The ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

The term "similarity transformation" is used either to refer to a geometric similarity, or to a matrix transformation that results in a similarity. A similarity ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

The first strong law of small numbers (Gardner 1980, Guy 1988, 1990) states "There aren't enough small numbers to meet the many demands made of them." The second strong law ...

In logic, the term "homomorphism" is used in a manner similar to but a bit different from its usage in abstract algebra. The usage in logic is a special case of a "morphism" ...

For two polynomials P_1(x)=a_mx^m+...+a_0 and P_2=b_nx^n+...+b_0 of degrees m and n, respectively, the Sylvester matrix is an (m+n)×(m+n) matrix formed by filling the matrix ...