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On the Analogue for maximally convergent polynomials of Jentzsch's theorem

Author: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
Publisher: Washington, D.C. : United States Air Force, Office of Scientific Research, 1958.
Series: United States. Air Force Office of Scientific Research Technical Note No., AFOSR TN 58-1086.
Edition/Format:   Print book : National government publication : EnglishView all editions and formats
Summary:
Although sequences of rational and analytic functions of the complex variable have been studied in some detail [2,3] regarding geometric degree of convergence, and convergent sequences of analytic functions have been basically studied [4] with reference to their zeros, no adequate applications to maximally convergent sequence of polynomials as such have been made. In particular there has been no special study of the  Read more...
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Additional Physical Format: Online version:
Walsh, J. L. (Joseph Leonard), 1895-1973.
Analogue for maximally convergent polynomials of Jentzsch's theorem
(OCoLC)1103317538
Material Type: Government publication, National government publication
Document Type: Book
All Authors / Contributors: J L Walsh; Harvard University.; United States. Air Force. Office of Scientific Research.
OCLC Number: 1077775751
Notes: "December 1958."
"AD No. 207 583."
Research supported with funding from the United States Air Force, Mathematics Division of the Office of Scientific Research, ARDC, under Contract No. AF 49(600)-1461, performed by Harvard University.
Division File Number: 1.38.
Description: 22 leaves ; 28 cm.
Series Title: United States. Air Force Office of Scientific Research Technical Note No., AFOSR TN 58-1086.
Other Titles: Technical Report Archive & Image Library (TRAIL)
Responsibility: J.L. Walsh, Harvard University.

Abstract:

Although sequences of rational and analytic functions of the complex variable have been studied in some detail [2,3] regarding geometric degree of convergence, and convergent sequences of analytic functions have been basically studied [4] with reference to their zeros, no adequate applications to maximally convergent sequence of polynomials as such have been made. In particular there has been no special study of the analogue of Jentzsch's theorem, that every point of the circle of convergence of a Taylor development is a limit point of zeros of the partial sums. The object of the present paper is to investigate specifically the zeros of maximally convergent sequences of polynomials, including in detail some illuminating special expansions.

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