Mathieun.

Brit.

/matˈjəː/, U.S.

/mætˈju/

Origin: From a proper name. Etymon: proper name Mathieu.

Etymology: < the name of Emile Léonard Mathieu (1835–90), French mathematician, who researched elliptically symmetrical systems.

Mathematics.

1. Mathieu's equation n. (also Mathieu equation, Mathieu differential equation) a differential equation arising in connection with elliptically symmetrical systems, having the form d²y/dx² + (a + b cos 2x)y = 0, where a and b are constants.

ΘΚΠ

the world > relative properties > number > calculus > [noun] > differential calculus > differential equations

Cauchy–Riemann equations1914

Mathieu's equation1915

1915 E. T. Whittaker & G. N. Watson Course Mod. Anal. (ed. 2) xix. 399 d²u/dz² + (a + 16q cos 2z)u = 0, where a and q are constants..is known as Mathieu's equation and..particular solutions of it are called Mathieu functions.

1957 L. Fox Numerical Solution Two-Point Boundary Probl. vii. 184 As a second example we consider the evaluation of an eigenvalue and eigenfunction of Mathieu's equation.

1962 Jrnl. Soc. Industr. & Appl. Math. 10 314 (heading) General perturbational solution of the Mathieu equation.

1969 Jrnl. Inst. Navigation 22 516 The Mathieu differential equation,..is the general system equation for both Schulerian and inertial navigations.

1998 Nature 12 Nov. 149/2 The Mathieu equation governs the forced motion of a swing, the stability of ships and columns, Faraday surface wave patterns on water, [etc.].

2. Mathieu function n. an even or odd periodic function that satisfies Mathieu's equation.

ΘΚΠ

the world > relative properties > number > calculus > [noun] > differential calculus > differential equations > solutions

particular integral1814

Bessel function1872

Mathieu function1915

1915 [see Mathieu's equation n. at sense 1].

1973 Jrnl. Math. Physics 14 199/2 We recommend that numerical integration of the Schrödinger equation for a −f²/r⁴ potential be avoided and that, instead, one makes use of linear combinations of Mathieu functions to represent the desired function for the appropriate region of space.

1987 SIAM Jrnl. Math. Anal. 18 1616 (heading) On a simplified asymptotic formula for the Mathieu function of the third kind.

This entry has been updated (OED Third Edition, March 2001; most recently modified version published online March 2022).

单词	mathieu
释义	Mathieun. Brit. /matˈjəː/, U.S. /mætˈju/ Origin: From a proper name. Etymon: proper name Mathieu. Etymology: < the name of Emile Léonard Mathieu (1835–90), French mathematician, who researched elliptically symmetrical systems. Mathematics. 1. Mathieu's equation n. (also Mathieu equation, Mathieu differential equation) a differential equation arising in connection with elliptically symmetrical systems, having the form d²y/dx² + (a + b cos 2x)y = 0, where a and b are constants. ΘΚΠ the world > relative properties > number > calculus > [noun] > differential calculus > differential equations Cauchy–Riemann equations1914 Mathieu's equation1915 1915 E. T. Whittaker & G. N. Watson Course Mod. Anal. (ed. 2) xix. 399 d²u/dz² + (a + 16q cos 2z)u = 0, where a and q are constants..is known as Mathieu's equation and..particular solutions of it are called Mathieu functions. 1957 L. Fox Numerical Solution Two-Point Boundary Probl. vii. 184 As a second example we consider the evaluation of an eigenvalue and eigenfunction of Mathieu's equation. 1962 Jrnl. Soc. Industr. & Appl. Math. 10 314 (heading) General perturbational solution of the Mathieu equation. 1969 Jrnl. Inst. Navigation 22 516 The Mathieu differential equation,..is the general system equation for both Schulerian and inertial navigations. 1998 Nature 12 Nov. 149/2 The Mathieu equation governs the forced motion of a swing, the stability of ships and columns, Faraday surface wave patterns on water, [etc.]. 2. Mathieu function n. an even or odd periodic function that satisfies Mathieu's equation. ΘΚΠ the world > relative properties > number > calculus > [noun] > differential calculus > differential equations > solutions particular integral1814 Bessel function1872 Mathieu function1915 1915 [see Mathieu's equation n. at sense 1]. 1973 Jrnl. Math. Physics 14 199/2 We recommend that numerical integration of the Schrödinger equation for a −f²/r⁴ potential be avoided and that, instead, one makes use of linear combinations of Mathieu functions to represent the desired function for the appropriate region of space. 1987 SIAM Jrnl. Math. Anal. 18 1616 (heading) On a simplified asymptotic formula for the Mathieu function of the third kind. This entry has been updated (OED Third Edition, March 2001; most recently modified version published online March 2022). < n.1915
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