A Course in Mathematical Analysis volume 21
A Course in Mathematical Analysis volume 21
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In our eReader you can find the full English version of the book. Read A Course in Mathematical Analysis volume 21 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Course in Mathematical Analysis volume 21
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Let T s = e 27rt s2/n, where n and s are integers; and let S n denote the sum T Q + T l + ---- \- T n _ i . Derive the formula (Apply the theorem on residues to the function $(z) = e 2niz2/n /(e Zlriz 1), taking for the boundary of integration the sides of the rectangle formed by the straight lines x = 0, x = n, y = + jR, y = R, and inserting two semicircumf erences of radius e about the points x = 0, x = n as centers, in order to avoid the poles z = and z n of the function 0(z) ; then let R be...come infinite. ) 22. Let/(z) be an analytic function in the interior of a closed curve T con taining the points a, 6, c, , 1. If a, /S, , X are positive integers, show that the sum of the residues of the function /(z) x-a\ x-b\f /x-JU with respect to the poles a, 6, c, , I is a polynomial F(x) of degree . . + \_ 1 satisfying the relations F(a)=/(o), F (a)=f(a), F(b)=f(b), (Make use of the relation JP (x) = /(x) + [ jj r) (z) efo]/2 Tri. ) 23*. Let/(z) be an analytic function in the interior of a circle C with center a.
What to read after A Course in Mathematical Analysis volume 21?
You can find similar books in the "Read Also" column, or choose other free books by Edouard Goursat to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Let T s = e 27rt s2/n, where n and s are integers; and let S n denote the sum T Q + T l + ---- \- T n _ i . Derive the formula (Apply the theorem on residues to the function $(z) = e 2niz2/n /(e Zlriz 1), taking for the boundary of integration the sides of the rectangle formed by the straight lines x = 0, x = n, y = + jR, y = R, and inserting two semicircumf erences of radius e about the points x = 0, x = n as centers, in order to avoid the poles z = and z n of the function 0(z) ; then let R be...come infinite. ) 22. Let/(z) be an analytic function in the interior of a closed curve T con taining the points a, 6, c, , 1. If a, /S, , X are positive integers, show that the sum of the residues of the function /(z) x-a\ x-b\f /x-JU with respect to the poles a, 6, c, , I is a polynomial F(x) of degree . . + \_ 1 satisfying the relations F(a)=/(o), F (a)=f(a), F(b)=f(b), (Make use of the relation JP (x) = /(x) + [ jj r) (z) efo]/2 Tri. ) 23*. Let/(z) be an analytic function in the interior of a circle C with center a.
What to read after A Course in Mathematical Analysis volume 21?
You can find similar books in the "Read Also" column, or choose other free books by Edouard Goursat to read onlineMoreLess
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