Accession Number:

AD0745018

Title:

Some Absolutely Monotonic and Completely Monotonic Functions.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

• Askey,Richard
• Pollard,Harry

Report Date:

1972-06-01

Pagination or Media Count:

14.0

Abstract:

The functions 1-rsup-2 lambda1-2xr r squaredsup-lambda are shown to be absolutely monotonic, or equivalently, that their power series have nonnegative coefficients for -1 or x or 1. One consequence is a simple proof of Kogbetliantzs theorem on positive Cesaro summability for ultraspherical series. Author

Descriptors:

• (*FUNCTIONS(MATHEMATICS)
• THEOREMS)
• POLYNOMIALS
• POWER SERIES
• OPERATORS(MATHEMATICS)

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE