| 释义 |
Mathieu, n. Math.
(mɑˈtjø, U.S. ˈmædjuː)
[The name of Emile Léonard Mathieu (1835–90), French mathematician.]
Used attrib. and in the possessive to designate concepts and entities mentioned by Mathieu or arising out of his work, as Mathieu('s) 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; Mathieu function, any even or odd periodic function satisfying Mathieu's equation.
1915Whittaker & Watson Course Mod. Analysis (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. Ibid. xix. 413 (heading) A second method of constructing the Mathieu function. 1957L. 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. 1962Jrnl. Soc. Industr. & Appl. Math. X. 314 (heading) General perturbational solution of the Mathieu equation. 1973Jrnl. Math. Physics XIV. 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. 1987SIAM Jrnl. Math. Anal. XVIII. 1616 (heading) On a simplified asymptotic formula for the Mathieu function of the third kind. |