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The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

Let R(z) be a rational function R(z)=(P(z))/(Q(z)), (1) where z in C^*, C^* is the Riemann sphere C union {infty}, and P and Q are polynomials without common divisors. The ...

In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row ...

Kurtosis is defined as a normalized form of the fourth central moment mu_4 of a distribution. There are several flavors of kurtosis, the most commonly encountered variety of ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

The intersection of two lines L_1 and L_2 in two dimensions with, L_1 containing the points (x_1,y_1) and (x_2,y_2), and L_2 containing the points (x_3,y_3) and (x_4,y_4), is ...

A linear recurrence equation is a recurrence equation on a sequence of numbers {x_n} expressing x_n as a first-degree polynomial in x_k with k<n. For example ...

Consider the process of taking a number, multiplying its digits, then multiplying the digits of numbers derived from it, etc., until the remaining number has only one digit. ...

Given a positive integer m>1, let its prime factorization be written m=p_1^(a_1)p_2^(a_2)p_3^(a_3)...p_k^(a_k). (1) Define the functions h(n) and H(n) by h(1)=1, H(1)=1, and ...

Approximants derived by expanding a function as a ratio of two power series and determining both the numerator and denominator coefficients. Padé approximations are usually ...