Search Results for ""

The integral int_0^1x^p(1-x)^qdx, called the Eulerian integral of the first kind by Legendre and Whittaker and Watson (1990). The solution is the beta function B(p+1,q+1).

The Bolyai expansion of a real number x is a nested root of the form x=a_0-1+RadicalBox[{{a, _, 1}, +, RadicalBox[{{a, _, 2}, +, RadicalBox[{{a, _, 3}, +, ...}, m]}, m]}, m], ...

A finite, increasing sequence of integers {a_1,...,a_m} such that (a_i-1)|(a_1...a_(m-1)) for i=1, ..., m, where m|n indicates that m divides n. A Carmichael sequence has ...

A method of determining coefficients alpha_l in an expansion y(x)=y_0(x)+sum_(l=1)^qalpha_ly_l(x) so as to nullify the values of an ordinary differential equation L[y(x)]=0 ...

If X is a normed linear space, then the set of continuous linear functionals on X is called the dual (or conjugate) space of X. When equipped with the norm ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

Two quantities y and x are said to be inversely proportional (or "in inverse proportion") if y is given by a constant multiple of 1/x, i.e., y=c/x for c a constant. This ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

For a catastrophically unstable recurrence in one direction, any seed values for consecutive x_j and x_(j+1) will converge to the desired sequence of functions in the ...