multinomial, a. and n. Alg.
(mʌltɪˈnəʊmɪəl)
Also 7 -nomall.
[f. multi- after binomial. Cf. F. multinome n., † multinomie adj.]
A. adj. Of an expression: Consisting of many (i.e. more than two) terms connected by the signs + or -.
multinomial theorem, a theorem discovered by De Moivre for the expression of any power of a multinomial without actual involution.
| 1608 R. Norton tr. Stevin's La Disme D, Ptolome and Iohannes Monta-regio haue not described their Tables of Arches, Chords, or Sines, in extreme perfection (as possibly they might haue done by Multinomall numbers) [orig. nombres multinomies]. 1697 Phil. Trans. XIX. 619 The infinite Number Multinomial. 1704 [see polynomial A. 1]. 1706 W. Jones Syn. Palmar. Matheseos 42 When the Dividend and Divisor are Multinomial Quantities..there may be a Common Multiplier of both. 1742 M{supc}Laurin Fluxions II. 761 An investigation of the binomial and multinomial theorems. 1858 Todhunter Algebra xxxvii. §530 By applying the multinomial theorem to find the coefficients of other powers of x. 1904 Jrnl. Math. Ser. ii. II. 478 The deficient multinomial expansion {ob}x1 + x2 + x3 + {ddd}{cb}p. |
B. n. A multinomial expression.
| 1674 S. Jeake Arith. (1696) 294 Where the composition hath more than two parts, the Compound is called a Polynomial or a Multinomial. 1697 Phil. Trans. XIX. 619 A Method of Raising an infinite Multinomial to any given Power... By Mr. Ab. De Moivre. 1742 M{supc}Laurin Fluxions II. 608 Mr. De Moivre's theorem for raising a multinomial to any power of the index n. 1858 Todhunter Algebra xxxvii. §528 The expansion of the proposed multinomial. |