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In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial, + +, The number 3 is a constant term. [1]
In this example a, b and c are coefficients of the polynomial. Since c occurs in a term that does not involve x, it is called the constant term of the polynomial and can be thought of as the coefficient of x 0. More generally, any polynomial term or expression of degree zero (no variable) is a constant. [5]: 18
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1] For example, the constant π may be defined as the ratio of the length of a circle's circumference to ...
A constant coefficient, also known as constant term or simply constant, is a quantity either implicitly attached to the zeroth power of a variable or not attached to other variables in an expression; for example, the constant coefficients of the expressions above are the number 3 and the parameter c, involved in 3=c ⋅ x 0.
The constant π (pi) has a natural definition in Euclidean geometry as the ratio between the circumference and diameter of a circle. It may be found in many other places in mathematics: for example, the Gaussian integral, the complex roots of unity, and Cauchy distributions in probability. However, its ubiquity is not limited to pure mathematics.
For example, a constant of integration is an arbitrary constant function that is added to a particular antiderivative to obtain the other antiderivatives. Because of the strong relationship between polynomials and polynomial functions , the term "constant" is often used to denote the coefficients of a polynomial, which are constant functions of ...
A term that doesn't contain any variables is called a ground term; a term that doesn't contain multiple occurrences of a variable is called a linear term. For example, 2+2 is a ground term and hence also a linear term, x⋅(n+1) is a linear term, n⋅(n+1) is a non-linear term. These properties are important in, for example, term rewriting.
The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted .