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The tangent function is defined by tanx=(sinx)/(cosx), (1) where sinx is the sine function and cosx is the cosine function. The notation tgx is sometimes also used ...

A function tau(n) related to the divisor function sigma_k(n), also sometimes called Ramanujan's tau function. It is defined via the Fourier series of the modular discriminant ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The Tutte 12-cage, also called the Benson graph (Exoo and Jajcay 2008), is the unique 12-cage graph, equivalent to the generalized hexagon GH(2,2) and alternately called the ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...

The binomial coefficient (n; k) is the number of ways of picking k unordered outcomes from n possibilities, also known as a combination or combinatorial number. The symbols ...

Let G be a group, and let S subset= G be a set of group elements such that the identity element I not in S. The Cayley graph associated with (G,S) is then defined as the ...

The divisor function sigma_k(n) for n an integer is defined as the sum of the kth powers of the (positive integer) divisors of n, sigma_k(n)=sum_(d|n)d^k. (1) It is ...

The m×n knight graph is a graph on mn vertices in which each vertex represents a square in an m×n chessboard, and each edge corresponds to a legal move by a knight (which may ...