BibTeX
@MISC{96doubleroots,
author = {},
title = {Double Roots of [\Gamma 1; 1] Power Series and Related Matters},
year = {1996}
}
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Abstract
Abstract For a given collection of distinct arguments ~ ` = (`1; : : : ; `t), multiplicities ~k = (k1; : : : ; kt); and a real interval I = [U; V] containing zero, we are interested in determining the smallest r for which there is a power series f(x) = 1 + P1n=1 anxn with coefficients an in I, and roots ff1 = re2ssi`1; : : : ; fft = re2ssi`t of order k1; : : : ; kt respectively. We denote this by r(~`; ~k; I). We describe the usual form of the extremal series (we give a sufficient condition which is also necessary when the extremal series possesses at least \Gamma Pti=1 ffi(`i)ki\Delta \Gamma 1 non-dependent coefficients strictly inside I, where ffi(`i) is 1 or 2 as ffi is real or complex).
