Introduction to the Theory of Analytic Functions |
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Introduction to the Theory of Analytic Functions James Harkness,Frank Morley No preview available - 2016 |
Common terms and phrases
a₁ absolute value absolutely convergent algebraic amplitude angle assigned axis b₁ b₂ bilinear transformation c₁ Cauchy's centre circle of convergence coefficients complex numbers constant continuous convergent series corresponding decimal defined definition denote domain elliptic function equal equation essential singular essential singular point expression finite number formula fractional fxdx geometric given Hence infinite infinity interval inverse irrational number Laurent series limit-point logarithm lower limit negative non-essential singular nth root one-valued analytic function one-valued function open region orthogonal P₁ pairs parallelogram path plane positive integer power series prove R₁ radius of convergence rational integral function real numbers real variable rectangle sequence singular point straight line stroke Suppose Taylor's theorem tends transcendental integral function uniformly convergent upper limit x-plane x₁ zero α₁
Popular passages
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Page ix - ... a foundation of algebraic truths. It is therefore not correct to turn around and, expressing myself briefly, use "transcendental...
Page 319 - Also we see that, by making n sufficiently large, we can make the fraction — - as small as we please. Thus by taking a sufficient number of terms the sum can be made to differ by as little as we please from 2. In the next article a more general case is discussed.
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Page 106 - Sc is also absolutely convergent, and its sum is the product of the sums of the two former series.
Page 16 - ... levers: the first has the fulcrum between the power and weight; in the second the weight acts between the fulcrum and the power; and in the third the power acts between the fulcrum and the weight. PROP. To find the conditions of equilibrium of two forces acting in the same plane on a lever. 93. Let the plane of the...
Page 6 - ... and not before the other. It is very important to notice that we have now a closed number-system. When we seek to separate the irrational objects as lying left or right of an object, either the object is rational, or if not it separates rational objects and is irrational ; in any case...
Page 117 - The idea that series of powers are as serviceable for algebra as for arithmetic was first worked out by Newton*, and in the theory of functions of a complex variable, as it now stands, the theory of such series is the solid foundation for the whole structure.
Page 5 - ... comes first. It is to be noticed that as we approach any of the natural objects there is no last fractional mark ; that is, whatever object we take there are always others between it and the natural object.