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Define S_n(x) = sum_(k=1)^(infty)(sin(kx))/(k^n) (1) C_n(x) = sum_(k=1)^(infty)(cos(kx))/(k^n), (2) then the Clausen functions are defined by ...

The Clebsch diagonal cubic is a cubic algebraic surface given by the equation x_0^3+x_1^3+x_2^3+x_3^3+x_4^3=0, (1) with the added constraint x_0+x_1+x_2+x_3+x_4=0. (2) The ...

A conic projection of points on a unit sphere centered at O consists of extending the line OS for each point S until it intersects a cone with apex A which tangent to the ...

The Copeland-Erdős constant is the constant with decimal expansion 0.23571113171923... (OEIS A033308) obtained by concatenating consecutive primes: 2, 23, 235, 2357, 235711, ...

A curtate cycloid, sometimes also called a contracted cycloid, is the path traced out by a fixed point at a radius b<a, where a is the radius of a rolling circle. Curtate ...

Form a sequence from an alphabet of letters [1,n] such that there are no consecutive letters and no alternating subsequences of length greater than d. Then the sequence is a ...

A method of determining the maximum number of positive and negative real roots of a polynomial. For positive roots, start with the sign of the coefficient of the lowest (or ...

The detour polynomial of a graph G is the characteristic polynomial of the detour matrix of G. Precomputed detour polynomials for many named graphs are available in the ...

Let f be a real-valued function defined on an interval [a,b] and let x_0 in (a,b). The four one-sided limits D^+f(x_0)=lim sup_(x->x_0+)(f(x)-f(x_0))/(x-x_0), (1) ...

Direct sums are defined for a number of different sorts of mathematical objects, including subspaces, matrices, modules, and groups. The matrix direct sum is defined by ...