The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5
The Boston Colloquium Lectures On Mathematics Delivered From September 2 to 5
Mass American Mathematical Society Colloquium 4th 1
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108 THE BOSTON COLLOQUIUM. The possibility that x should, in addition, be a singular point has been pointed out since by Lindelof. Although HadamarcVs proof of the theorem is not a compli- cated one, I shall present here a still simpler proof given by BoreL* Let II and R' be the radii of convergence of (1) and (2) respec- tively, and take a number p such that 7i/p > 1 ft'. If then | zx | = | px | l/R' } the product of
+ afo + "A"- 2 + Consider now the integral (>) 'llTT, in whic
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h c is a closed path surrounding the origin and contained within the circular ring. As long as z in its plane lies within a circle of radius p ).
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