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One of the quantities lambda_i appearing in the Gauss-Jacobi mechanical quadrature. They satisfy lambda_1+lambda_2+...+lambda_n = int_a^bdalpha(x) (1) = alpha(b)-alpha(a) (2) ...

The Franel numbers are the numbers Fr_n=sum_(k=0)^n(n; k)^3, (1) where (n; k) is a binomial coefficient. The first few values for n=0, 1, ... are 1, 2, 10, 56, 346, ... (OEIS ...

In general, a remainder is a quantity "left over" after performing a particular algorithm. The term is most commonly used to refer to the number left over when two integers ...

A connected graph G is said to be t-tough if, for every integer k>1, G cannot be split into k different connected components by the removal of fewer than tk vertices. The ...

The Jacobsthal numbers are the numbers obtained by the U_ns in the Lucas sequence with P=1 and Q=-2, corresponding to a=2 and b=-1. They and the Jacobsthal-Lucas numbers (the ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

Taylor's inequality is an estimate result for the value of the remainder term R_n(x) in any n-term finite Taylor series approximation. Indeed, if f is any function which ...

The term cube is used in topology to denote the Cartesian product of any (finite or infinite) number of copies of the closed interval [0,1] equipped with the product topology ...

The only linear associative algebra in which the coordinates are real numbers and products vanish only if one factor is zero are the field of real numbers, the field of ...

When the index nu is real, the functions J_nu(z), J_nu^'(z), Y_nu(z), and Y_nu^'(z) each have an infinite number of real zeros, all of which are simple with the possible ...