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The inverse tangent is the multivalued function tan^(-1)z (Zwillinger 1995, p. 465), also denoted arctanz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. 311; ...

There are infinitely many primes m which divide some value of the partition function P.

A pair of closed form functions (F,G) is said to be a Wilf-Zeilberger pair if F(n+1,k)-F(n,k)=G(n,k+1)-G(n,k). (1) The Wilf-Zeilberger formalism provides succinct proofs of ...

The ABC (atom-bond connectivity) energy of a graph is defined as the graph energy of its ABC matrix, i.e., the sum of the absolute values of the eigenvalues of its ABC matrix.

A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

It is conjectured that every tree with e edges whose nodes are all trivalent or monovalent can be given a "magic" labeling such that the integers 1, 2, ..., e can be assigned ...

An analog of the determinant for number triangles defined as a signed sum indexed by set partitions of {1,...,n} into pairs of elements. The Pfaffian is the square root of ...

Let P be a prime ideal in D_m not containing m. Then (Phi(P))=P^(sumtsigma_t^(-1)), where the sum is over all 1<=t<m which are relatively prime to m. Here D_m is the ring of ...

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...