A Course in Mathematical Analysis, Τόμος 2Ginn, 1916 |
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ Abelian integral absolute value absolutely convergent algebraic analytic extension angle approaches zero b₁ becomes infinite C₁ C₂ circle of convergence circle of radius closed curve coefficients complex variables convergent series coördinates corresponding critical points cubic deduce definite integral degree denotes derivative describes double points elliptic function equal equation F(x essentially singular point example expression final value formula func function analytic function f(z Hence infinite number initial value integral function integral taken interior Let us consider let us suppose limit loop m₁ neighborhood obtain origin as center parallelogram of periods parameter plane point at infinity poles polynomial positive number power series preceding quotient rational function region relation replace represents residue roots segment single-valued analytic function singular points straight line theorem tion uniformly convergent y₁ πί
Δημοφιλή αποσπάσματα
Σελίδα 23 - N can be written in one and only one way in the form of a sum of powers of 2.
Σελίδα 151 - ... no longer has any poles on the boundary of the parallelogram. When we have occasion to integrate an elliptic function f(u) along the boundary of the parallelogram of periods, we shall always suppose, if it is necessary, that the parallelogram has been displaced in such a way that f(u) has no longer any poles on its boundary.
Σελίδα 52 - R* sin2 0 (d<p2 + -~] , and we shall set We obtain thus what is called Mercator's projection, in which the meridians are represented by parallels to the axis OY, and the parallels of latitude by segments of straight lines parallel to OX. To obtain the whole surface of...
Σελίδα 7 - Analytic functions. If f(x) is a function of a real variable x which has a derivative, the quotient approaches f(x) when h approaches zero. Let us determine in the same way under what conditions the quotient AM _ AP + «A(j A« Ax + iAy will approach a definite limit when the absolute value of Az approaches /wo, that is, when A.
Σελίδα 6 - Then, /to) the last equality following from the fact that the absolute value of a product is equal to the product of the absolute values [Eq.
Σελίδα 9 - Oy oy ox It is important to notice that neither of the pair of functions P(x, y), Q(x, y) can be taken arbitrarily. In fact, if P and Q have derivatives of the second order, and if we differentiate the first of the relations (1) with respect to x, and the second with respect to y, we have, adding the two resulting equations...
Σελίδα 165 - If a zero as is not a half-period, it will be made to appear in the sequence a,, av . . ., an as often as there are units in its degree of multiplicity. If the zero av for example, is a half-period, it will be a zero of even order 2 r (§ 68, notes). We shall make this zero appear only r times in the sequence...