Riccatin.

Brit.

/rɪˈkati/, U.S.

/rəˈkædi/

Forms: 1700s– Riccati, 1800s– Ricatti (irregular), 1900s– Riccatti (irregular).

Origin: From a proper name; modelled on a French lexical item. Etymon: proper name Riccati.

Etymology: < the name of Count Jacopo Francesco Riccati (1676–1754), Italian mathematician, who published the first equation of this type, after French equation de Riccati (d'Alembert 1774).

Mathematics.

attributive, in the genitive, and with of. Designating certain kinds of differential equation; spec. a first-order non-linear differential equation of the form ^dy/ _dx = P(x)y² + Q(x)y + Z(x), which can be reduced to a second-order linear differential equation.Two other kinds of differential equation that go under this name are (a) a first-order linear differential equation of the form ^dy/ _dx = axⁿ + by², where n is an integer and a and b are constants; (b) a second-order non-linear differential equation of the form x²^d²y/ _dx² + (x² - n(n+1))y = 0, where n is an integer.

ΚΠ

1791 Monthly Rev. 4 484 The equation, found by the curve described, is of that form, which is called the differential equation of Riccati.

1802 Crit. Rev. 36 490 The historian, in the next article, first treats of the different forms of fluxions of the first order..and then of what was called Riccati's equation.

1854 B. Price Treat. Infinitesimal Calculus II. xiii. 437 The Equation of Riccati also admits of transformation into a differential equation of the second order.

1918 Trans. Amer. Math. Soc. 19 183 This gives an equation of Riccati for the determination of V₂.

1928 Proc. Royal Soc. A. 118 643 In his treatment of equation (1) he expands the Riccatti equation round the irregular singularity at infinity.

1995 Statist. Sci. 10 95/1 Some highly technical machinery involving the solution of a matrix Ricatti equation..is then invoked to obtain the survival function.

2006 B. Z. Katsenelenbaum High-frequency Electrodynamics ii. 57 ρ(z) satisfies the first-order nonlinear differential equation of Riccati.

This is a new entry (OED Third Edition, June 2010; most recently modified version published online March 2022).

单词	riccati
释义	Riccatin. Brit. /rɪˈkati/, U.S. /rəˈkædi/ Forms: 1700s– Riccati, 1800s– Ricatti (irregular), 1900s– Riccatti (irregular). Origin: From a proper name; modelled on a French lexical item. Etymon: proper name Riccati. Etymology: < the name of Count Jacopo Francesco Riccati (1676–1754), Italian mathematician, who published the first equation of this type, after French equation de Riccati (d'Alembert 1774). Mathematics. attributive, in the genitive, and with of. Designating certain kinds of differential equation; spec. a first-order non-linear differential equation of the form ^dy/ _dx = P(x)y² + Q(x)y + Z(x), which can be reduced to a second-order linear differential equation.Two other kinds of differential equation that go under this name are (a) a first-order linear differential equation of the form ^dy/ _dx = axⁿ + by², where n is an integer and a and b are constants; (b) a second-order non-linear differential equation of the form x²^d²y/ _dx² + (x² - n(n+1))y = 0, where n is an integer. ΚΠ 1791 Monthly Rev. 4 484 The equation, found by the curve described, is of that form, which is called the differential equation of Riccati. 1802 Crit. Rev. 36 490 The historian, in the next article, first treats of the different forms of fluxions of the first order..and then of what was called Riccati's equation. 1854 B. Price Treat. Infinitesimal Calculus II. xiii. 437 The Equation of Riccati also admits of transformation into a differential equation of the second order. 1918 Trans. Amer. Math. Soc. 19 183 This gives an equation of Riccati for the determination of V₂. 1928 Proc. Royal Soc. A. 118 643 In his treatment of equation (1) he expands the Riccatti equation round the irregular singularity at infinity. 1995 Statist. Sci. 10 95/1 Some highly technical machinery involving the solution of a matrix Ricatti equation..is then invoked to obtain the survival function. 2006 B. Z. Katsenelenbaum High-frequency Electrodynamics ii. 57 ρ(z) satisfies the first-order nonlinear differential equation of Riccati. This is a new entry (OED Third Edition, June 2010; most recently modified version published online March 2022). < n.1791
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