Outline of Proof
After subtracting a constant from, we may assume that . Let . Then substituting and performing a simple manipulation of the series results in
Given, pick n large enough so that for all and note that
when z lies within the given Stoltz angle. Whenever z is sufficiently close to 1 we have
so that when z is both sufficiently close to 1 and within the Stoltz angle.
Read more about this topic: Abel's Theorem
Famous quotes containing the words outline of, outline and/or proof:
“The outline of the city became frantic in its effort to explain something that defied meaning. Power seemed to have outgrown its servitude and to have asserted its freedom. The cylinder had exploded, and thrown great masses of stone and steam against the sky.”
—Henry Brooks Adams (1838–1918)
“The outline of the city became frantic in its effort to explain something that defied meaning. Power seemed to have outgrown its servitude and to have asserted its freedom. The cylinder had exploded, and thrown great masses of stone and steam against the sky.”
—Henry Brooks Adams (1838–1918)
“There are some persons in this world, who, unable to give better proof of being wise, take a strange delight in showing what they think they have sagaciously read in mankind by uncharitable suspicions of them.”
—Herman Melville (1819–1891)