Vol. 89, No. 1, 1980

Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Mapping properties, growth, and uniqueness of Vieta (infinite cosine) products

Kenneth Barry Stolarsky

Vol. 89 (1980), No. 1, 209–227

The natural logarithm of z can be written as an infinite product involving iterated square roots of z. A Vieta product is defined to be a more general infinite product involving z raised to arbitrary fractional powers. Restricted to the unit circle, Vieta products generalize infinite cosine products studied by Salem and others in connection with PV -numbers. Vieta products are shown to have conformal mapping, monotonicity, and growth properties very similar to those of the natural logarithm. By using certain properties of Eulerian polynomials, the exponents of z in a Vieta product are shown to be unique in a strong sense.

Mathematical Subject Classification 2000
Primary: 30E99
Secondary: 40A20
Received: 17 September 1979
Published: 1 July 1980
Kenneth Barry Stolarsky