Search Results for ""

A polynomial sequence p_n(x) is called the basic polynomial sequence for a delta operator Q if 1. p_0(x)=1, 2. p_n(0)=0 for all n>0, 3. Qp_n(x)=np_(n-1)(x). If p_n(x) is a ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

Three types of n×n matrices can be obtained by writing Pascal's triangle as a lower triangular matrix and truncating appropriately: a symmetric matrix S_n with (S)_(ij)=(i+j; ...

A generalization of simple majority voting in which a list of quotas {q_0,...,q_n} specifies, according to the number of votes, how many votes an alternative needs to win ...

The trinomial triangle is a number triangle of trinomial coefficients. It can be obtained by starting with a row containing a single "1" and the next row containing three 1s ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...