holomorphic, a.
(hɒləʊˈmɔːfɪk)
[f. holo- + Gr. µορϕ-ή shape, form + -ic.]
1. Cryst. The same as holohedral or holosymmetrical, esp. as distinguished from hemimorphic.
2. Math. Said of a function which is monogenic, uniform, and continuous.
| 1880 G. S. Carr Synops. Math. Index 886 Holomorphic functions. 1893 Forsyth Theory of Functions 15 When a function is called holomorphic without any limitation, the usual implication is that the character is preserved over the whole of the plane which is not at infinity. |
So holoˈmorphically adv., in such a way as to be or remain holomorphic (in sense 2); ˈholomorphy, ‘the character of being holomorphic’ (Cent. Dict.).
| 1957 Pacific Jrnl. Math. VII. 812 There exist domains..such that all G-holomorphic functions can be continued G-holomorphically into a larger domain. Ibid. 820 If D is a domain of holomorphy, then the set C..belongs to D. 1963 Standring & Shutrick tr. Cartan's Elem. Theory of Analytic Functions ii. 73 For functions of a complex variable, there is an equivalence between holomorphy and analyticity. 1966 Mathematical Rev. XXXI. 33/2 A closed holomorphic differential p-form in x, holomorphically varying with y. |