| 释义 |
Gudermannian, a. and n. Math.|gjuːdəˈmænɪən|
[f. the name of Gudermann, a German mathematician who first investigated these functions.]
A. adj. Applied (by Cayley) to the function (denoted by the letters gd) defined by the equation x = log tan (1/4 π + ½ gd x).
B. n. A Gudermannian function.
The circular functions of the Gudermannian of any quantity correspond to the hyperbolic functions of that quantity (e.g. tan gd x = sinh x, etc.).
1876Cayley Elliptic Functions 56 The Gudermannian. Ibid., Instead of the general function am u, we have the gudermannian gd u, giving rise to the two functions sin gd u and cos gd u, or say sg u and cg u. 1888Greenhill Chapter Integral Calculus 28 The Gudermannian function connects the circular and hyperbolic functions. |