A Course in Mathematical Analysis, Τόμος 2,Μέρος 1Ginn, 1916 |
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ absolute value absolutely convergent analytic function angle approaches zero b₁ becomes infinite boundary C₁ circle of convergence circle of radius closed curve coefficients complex quantity complex variable continuous function coördinates corresponding critical points definite integral degree denote derivative determined elliptic function equal equation essentially singular point example expression finite formula func function analytic function f(z Hence infinite number initial value integral function integral taken interior less Let f(z Let us consider let us suppose limit Log ƒ logarithm loop m₁ neighborhood obtain origin as center parallelogram path of integration periods plane point at infinity poles polynomial positive number positive sense power series preceding quotient rational function region relation replace represents residue straight line term theorem tion uniformly convergent y₁ πί др дх
Δημοφιλή αποσπάσματα
Σελίδα 23 - N can be written in one and only one way in the form of a sum of powers of 2. We have, then, if z | < 1 , (16) 1-z which can also be very easily obtained by means of the identity 1-z2* 1-z = (1 + z) (1 + z!) (1 + z4) . . . (1 + z2
Σελίδα 110 - This number is equal to where the integral is taken in the positive sense along the boundary of the neighborhood of the point at infinity. But here, the neighborhood of the point at infinity being the part of the plane exterior to C, the corresponding positive sense is that opposite to the usual sense. Indeed, this integral reduces to and, when z describes the circle C in the desired sense, the angle of z diminishes by 2 TT, which gives — A1 as the value of the integral.
Σελίδα 53 - Example 3. Map of an anchor ring. Consider the anchor ring generated by the revolution of a circle of radius R about an axis situated in its own plane at a distance a from its center, where a > R. Taking the axis of revolution for the axis of z, and the median plane of the anchor ring for the...
Σελίδα 186 - CLEBSCH, Ueber diejenigen Curven, deren Coordinaten sich als elliptische Functionen eines Parameters darstellen lassen (Crette's Journal, Vol.