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Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

The negabinary representation of a number n is its representation in base -2 (i.e., base negative 2). It is therefore given by the coefficients a_na_(n-1)...a_1a_0 in n = ...

Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...

Samuel Pepys wrote Isaac Newton a long letter asking him to determine the probabilities for a set of dice rolls related to a wager he planned to make. Pepys asked which was ...

Newton's forward difference formula is a finite difference identity giving an interpolated value between tabulated points {f_p} in terms of the first value f_0 and the powers ...

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

The noncentral chi-squared distribution with noncentrality parameter lambda is given by P_r(x) = ...

A set in which no element divides the sum of any nonempty subset of the other elements. For example, {2,3,5} is dividing, since 2|(3+5) (and 5|(2+3)), but {4,6,7} is ...

Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As ...