Timeline for Raising coefficients of a power series to some power
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2015 at 2:15 | comment | added | batconjurer | Now I know the name for this! I looked at the papers and I think I can confirm what Timothy Chow was saying: namely that the degree of the denominator increases by a factor of $\kappa$ | |
| Apr 20, 2015 at 2:11 | vote | accept | batconjurer | ||
| Apr 19, 2015 at 21:20 | answer | added | Timothy Chow | timeline score: 3 | |
| Apr 19, 2015 at 19:47 | comment | added | Douglas Zare |
David Handelman pointed out that this is the Hadamard product of P with itself. Hadamard proved some results that might be useful, perhaps in J. Hadamard, Th´eoreme sur les s´eries entieres, Acta. Math. 22 (1899) 55–63. I haven't tracked down that reference yet, though papers that cite it mention some theorems that might be useful.
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| Apr 19, 2015 at 14:13 | comment | added | David Handelman | There are results on asymptotic behaviour (approaching 1 along the reals) for this type of function: D Handelman, Karamata Renewed and Local Limit Results Canad. J. Math. Vol. 58 (5), 2006 pp. 1026–1094, cms.math.ca/openaccess/cjm/v58/handelman3372.pdf, where the term used is Hadamard power, pp 24--25 (and Hadamard products are also discussed); this may be helpful. This applies to a special family of analytic functions, although among other things it requires nicely behaved nonnegative entries in the Maclaurin expansion. | |
| Apr 19, 2015 at 4:06 | review | Close votes | |||
| Apr 19, 2015 at 8:21 | |||||
| Apr 19, 2015 at 2:39 | history | asked | batconjurer | CC BY-SA 3.0 |