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The q-binomial coefficient is a q-analog for the binomial coefficient, also called a Gaussian coefficient or a Gaussian polynomial. A q-binomial coefficient is given by [n; ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

The n-centipede graph, n-centipede tree, n-comb graph (Seoud and Youssef 2017), or simply "n-centipede," is the tree on 2n nodes obtained by joining the bottoms of n copies ...

Champernowne's constant C=0.12345678910111213... (1) (OEIS A033307) is the number obtained by concatenating the positive integers and interpreting them as decimal digits to ...

Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...

The happy end problem, also called the "happy ending problem," is the problem of determining for n>=3 the smallest number of points g(n) in general position in the plane ...

The hemicubical graph is the skeleton of the hemicube. It has 7 vertices, 11 edges, and 6 faces. It is implemented in the Wolfram Language as GraphData["HemicubicalGraph"].

Let two points x and y be picked randomly from a unit n-dimensional hypercube. The expected distance between the points Delta(n), i.e., the mean line segment length, is then ...

A kayak paddle graph KP(k,m,l) is the graph obtained by joining cycle graphs C_k and C_m by a path of length l (Gallian 2018). KP(3,3,1) is isomorphic to the 3-barbell graph. ...

The Mangoldt function is the function defined by Lambda(n)={lnp if n=p^k for p a prime; 0 otherwise, (1) sometimes also called the lambda function. exp(Lambda(n)) has the ...