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The apodization function A(x)=1-(x^2)/(a^2). (1) Its full width at half maximum is sqrt(2)a. Its instrument function is I(k) = 2asqrt(2pi)(J_(3/2)(2pika))/((2pika)^(3/2)) (2) ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

A variant of the Pollard p-1 method which uses Lucas sequences to achieve rapid factorization if some factor p of N has a decomposition of p+1 in small prime factors.

The Zeckendorf representation of a positive integer n is a representation of n as a sum of nonconsecutive distinct Fibonacci numbers, n=sum_(k=2)^Lepsilon_kF_k, where ...

The Zolotarev-Schur constant is given by sigma = 1/(c^2)[1-(E(c))/(K(c))]^2 (1) = 0.3110788667048... (2) (OEIS A143295), where K(c) is a complete elliptic integral of the ...

The de Bruijn constant, also called the Copson-de Bruijn constant, is the minimal constant c=1.1064957714... (OEIS A113276) such that the inequality ...

A k-coloring of a graph G is a vertex coloring that is an assignment of one of k possible colors to each vertex of G (i.e., a vertex coloring) such that no two adjacent ...

Graphs corresponding to closed walks of length k are known as k-cyclic graphs, or C_k-graphs for short. C_k-graphs are connected by definition. The numbers of C_k-graphs for ...

Van der Corput's constant is given by m = 2sqrt(2)int_0^(sqrt(pi/2-c))cos(x^2+c)dx (1) = 2pi[coscC(phi)-sincS(phi)] (2) = 3.3643175781... (3) (OEIS A143305), where C(x) and ...

The set R union {+infty,-infty} obtained by adjoining two improper elements to the set R of real numbers is normally called the set of (affinely) extended real numbers. ...