英语词汇“reversion of series”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

b. Mathematics. More fully reversion of series. The determination of the power series of an inverse function in terms of the power series of the original function.E.g. given a function y = f(x) expressed as a series a + bx + cx² + …, reversion consists of finding the coefficients of the series that gives x in terms of y: x = g(y) = A + By + Cy² + …, where A, B, C, etc., are expressed in terms of a, b, c, etc.

ΘΚΠ

the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > inverting

alternate proportion1570

inversion1645

transposition1664

reversion1698

involution1916

1698 A. de Moivre in Philos. Trans. (Royal Soc.) 20 191 This Theorem may be applied to what is called the Reversion of Series, such as finding the Number from its Logarithm given; the Sine from the Arc.

1737 Gentleman's Mag. Mar. 135/1 He himself has given us the Value of v above by Reversion.

1797 Encycl. Brit. XVII. 297/2 Reversion of Series is the method of finding the value of the quantity whose several powers are involved in a series, in terms of the quantity which is equal to the given series.

1841 Penny Cycl. XIX. 437/1 If y be a given series of powers of x, the determination of x in a series of functions of y is not called inversion, but reversion.

1919 F. Cajori Hist. Math. (ed. 2) 227 Thomas Simpson determined roots by reversion of series in 1743 and by infinite series in 1745.

2003 A. Heck Introd. Maple (ed. 3) xi. 272 A problem..which can be solved as a problem of series reversion, is the computation of the series expansion of the solution of Kepler's equation.

单词	reversion of series
释义	> as lemmas reversion of series b. Mathematics. More fully reversion of series. The determination of the power series of an inverse function in terms of the power series of the original function.E.g. given a function y = f(x) expressed as a series a + bx + cx² + …, reversion consists of finding the coefficients of the series that gives x in terms of y: x = g(y) = A + By + Cy² + …, where A, B, C, etc., are expressed in terms of a, b, c, etc. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [noun] > correspondence > inverting alternate proportion1570 inversion1645 transposition1664 reversion1698 involution1916 1698 A. de Moivre in Philos. Trans. (Royal Soc.) 20 191 This Theorem may be applied to what is called the Reversion of Series, such as finding the Number from its Logarithm given; the Sine from the Arc. 1737 Gentleman's Mag. Mar. 135/1 He himself has given us the Value of v above by Reversion. 1797 Encycl. Brit. XVII. 297/2 Reversion of Series is the method of finding the value of the quantity whose several powers are involved in a series, in terms of the quantity which is equal to the given series. 1841 Penny Cycl. XIX. 437/1 If y be a given series of powers of x, the determination of x in a series of functions of y is not called inversion, but reversion. 1919 F. Cajori Hist. Math. (ed. 2) 227 Thomas Simpson determined roots by reversion of series in 1743 and by infinite series in 1745. 2003 A. Heck Introd. Maple (ed. 3) xi. 272 A problem..which can be solved as a problem of series reversion, is the computation of the series expansion of the solution of Kepler's equation. extracted from reversionn.¹ < as lemmas
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> as lemmas