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N. Nielsen (1909) and Ramanujan (Berndt 1985) considered the integrals a_k=int_1^2((lnx)^k)/(x-1)dx. (1) They found the values for k=1 and 2. The general constants for k>3 ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

The doubly noncentral F-distribution describes the distribution (X/n_1)/(Y/n_2) for two independently distributed noncentral chi-squared variables X:chi_(n_1)^2(lambda_1) and ...

The norm of a mathematical object is a quantity that in some (possibly abstract) sense describes the length, size, or extent of the object. Norms exist for complex numbers ...

If T is a linear transformation of R^n, then the null space Null(T), also called the kernel Ker(T), is the set of all vectors X such that T(X)=0, i.e., Null(T)={X:T(X)=0}. ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

The octahedral equation, by way of analogy with the icosahedral equation, is a set of related equations derived from the projective geometry of the octahedron. Consider an ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...

A (general) octahedron is a polyhedron having eight faces. Examples include the 4-trapezohedron, augmented triangular prism (Johnson solid J_(49)), bislit cube, Dürer solid, ...

The odd divisor function sigma_k^((o))(n)=sum_(d|n; d odd)d^k (1) is the sum of kth powers of the odd divisors of a number n. It is the analog of the divisor function for odd ...