Definition of Indeterminate coefficients. Meaning of Indeterminate coefficients. Synonyms of Indeterminate coefficients

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Definition of Indeterminate coefficients

Indeterminate coefficients
Indeterminate In`de*ter"mi*nate, a. [L. indeterminatus.] Not determinate; not certain or fixed; indefinite; not precise; as, an indeterminate number of years. --Paley. Indeterminate analysis (Math.), that branch of analysis which has for its object the solution of indeterminate problems. Indeterminate coefficients (Math.), coefficients arbitrarily assumed for convenience of calculation, or to facilitate some artifice of analysis. Their values are subsequently determined. Indeterminate equation (Math.), an equation in which the unknown quantities admit of an infinite number of values, or sets of values. A group of equations is indeterminate when it contains more unknown quantities than there are equations. Indeterminate inflorescence (Bot.), a mode of inflorescence in which the flowers all arise from axillary buds, the terminal bud going on to grow and sometimes continuing the stem indefinitely; -- called also acropetal, botryose, centripetal, & indefinite inflorescence. --Gray. Indeterminate problem (Math.), a problem which admits of an infinite number of solutions, or one in which there are fewer imposed conditions than there are unknown or required results. Indeterminate quantity (Math.), a quantity which has no fixed value, but which may be varied in accordance with any proposed condition. Indeterminate series (Math.), a series whose terms proceed by the powers of an indeterminate quantity, sometimes also with indeterminate exponents, or indeterminate coefficients. -- In`de*ter"mi*nate*ly adv. -- In`de*ter"mi*nate*ness, n.

Meaning of Indeterminate coefficients from wikipedia

- polynomials, requiring neither coefficients nor exponents. Coefficients are redundant because 1 is the only nonzero coefficient. Exponents are redundant because...
- polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition...
- ai{\displaystyle a_{i}} are called the coefficients of the polynomial. Two such polynomials are equal only if the corresponding coefficients are equal. In contrast,...
- obtained by replacing in the generic resultant the indeterminate coefficients by the actual coefficients of the P i . {\displaystyle P_{i}.} The main property...
- found by equating the rational function to a Taylor series with indeterminate coefficients, and collecting like terms after clearing the denominator. For...
- polynomial P(x) of degree less than n(m + 1) with indeterminate coefficients; that is, the coefficients of P(x) are n(m + 1) new variables. Then, by writing...
- differential equations to power series with indeterminate coefficients, one may deduce recurrence relations for the coefficients of the Taylor series of the sine...
- from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the...
- The integers x and y are called Bézout coefficients for (a, b); they are not unique. A pair of Bézout coefficients can be computed by the extended Euclidean...
- In mathematics, particularly in algebra, an indeterminate system is a system of simultaneous equations (e.g., linear equations) which has more than one...