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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.
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]
[1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4] Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
A coefficient is a numerical value, or letter representing a numerical constant, that multiplies a variable (the operator is omitted). A term is an addend or a summand, a group of coefficients, variables, constants and exponents that may be separated from the other terms by the plus and minus operators. [9] Letters represent variables and ...
has a constant term of −4, which can be considered to be the coefficient of , where the variables are eliminated by being exponentiated to 0 (any non-zero number exponentiated to 0 becomes 1). For any polynomial, the constant term can be obtained by substituting in 0 instead of each variable; thus, eliminating each variable.
A term with no indeterminates and a polynomial with no indeterminates are called, respectively, a constant term and a constant polynomial. [b] The degree of a constant term and of a nonzero constant polynomial is 0. The degree of the zero polynomial 0 (which has no terms at all) is generally treated as not defined (but see below).
Note that if the constant term in the original third equation had been anything other than –7, the values (a, b) = (1, 1) that satisfied the first two equations in the parameters would not have satisfied the third one (a – 8b = constant), so there would exist no a, b satisfying all three equations in the parameters, and therefore the third ...
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.