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The word polynomial joins two diverse roots: the Greek poly, meaning "many", and the Latin nomen, or "name". It was derived from the term binomial by replacing the Latin root bi-with the Greek poly-. That is, it means a sum of many terms (many monomials). The word polynomial was first used in the 17th century. [6]
In mathematics, Brenke polynomials are special cases of generalized Appell polynomials, and Brenke–Chihara polynomials are the Brenke polynomials that are also orthogonal polynomials. Brenke ( 1945 ) introduced sequences of Brenke polynomials P n , which are special cases of generalized Appell polynomials with generating function of the form
In mathematics, Meixner polynomials (also called discrete Laguerre polynomials) are a family of discrete orthogonal polynomials introduced by Josef Meixner . They are given in terms of binomial coefficients and the (rising) Pochhammer symbol by
For example, in Chapter 1 of Hartshorne a variety over an algebraically closed field is defined to be a quasi-projective variety, [1]: 15 but from Chapter 2 onwards, the term variety (also called an abstract variety) refers to a more general object, which locally is a quasi-projective variety, but when viewed as a whole is not necessarily quasi ...
For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...
In general, when ℓ and m are integers, the regular solutions are sometimes called "associated Legendre polynomials", even though they are not polynomials when m is odd. The fully general class of functions with arbitrary real or complex values of ℓ and m are Legendre functions. In that case the parameters are usually labelled with Greek ...
Any symmetric polynomial in n indeterminates can be used to construct a compatible family of symmetric polynomials, using the homomorphisms ρ i for i < n to decrease the number of indeterminates, and φ i for i ≥ n to increase the number of indeterminates (which amounts to adding all monomials in new indeterminates obtained by symmetry from ...
A polynomial f with coefficients in F q (symbolically written as f ∈ F q [x]) is a permutation polynomial of F q if the function from F q to itself defined by () is a permutation of F q. [4] Due to the finiteness of F q, this definition can be expressed in several equivalent ways: [5]