Lectures Introductory to the Theory of Functions of Two Complex Variables; Delivered to the University of Calcutta During January And February 1913
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Consequently, we have and therefore when the double integration is taken over any simple closed region in the plane of the real variables p, q.
Ill] Abel's theorem 197 This is a restricted extension of a part of Abel's general theorem on the sum of integrals. The result is true, even if the integral /] -J dpdq is not everywhere finite, that is, if the integral is not of the first kind*. The conditions, which have been imposed upon the integral, are that it is to be finite for all places which a...re ordinary for the equations /= 0, g = 0, all infinite places being supposed included among these ordinary places.
* It should be added that, by a different method, Picard (I. c, t. i, p. 190) obtains this extension for double integrals of the first kind (that is, integrals which are everywhere finite) when there is a single fundamental equation f(w, z, z')=:0.
CHAPTER VII Level Places of Two Uniform Functions 112. Hitherto, save for rare exceptions, only individual functions of two variables have been considered at any one time ; and we have seen that there exist continuous aggregates of places where a function has an assigned level value or a zero value.
What to read after Lectures Introductory to the Theory of Functions of Two Complex Variables; Delivered to the University of Calcutta During January And February 1913?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Consequently, we have and therefore when the double integration is taken over any simple closed region in the plane of the real variables p, q.
Ill] Abel's theorem 197 This is a restricted extension of a part of Abel's general theorem on the sum of integrals. The result is true, even if the integral /] -J dpdq is not everywhere finite, that is, if the integral is not of the first kind*. The conditions, which have been imposed upon the integral, are that it is to be finite for all places which a...re ordinary for the equations /= 0, g = 0, all infinite places being supposed included among these ordinary places.
* It should be added that, by a different method, Picard (I. c, t. i, p. 190) obtains this extension for double integrals of the first kind (that is, integrals which are everywhere finite) when there is a single fundamental equation f(w, z, z')=:0.
CHAPTER VII Level Places of Two Uniform Functions 112. Hitherto, save for rare exceptions, only individual functions of two variables have been considered at any one time ; and we have seen that there exist continuous aggregates of places where a function has an assigned level value or a zero value.
What to read after Lectures Introductory to the Theory of Functions of Two Complex Variables; Delivered to the University of Calcutta During January And February 1913?
You can find similar books in the "Read Also" column, or choose other free books by Forsyth, Andrew Russell, 1858-1942 to read onlineMoreLess
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