http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series Comments for "Criterion for boundedness of power series" en http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment-7182 <p>The sine function is in the class mentioned.</p> Thu, 21 Jun 2012 22:57:43 +0200 Anonymous comment 7182 at http://openproblemgarden.org http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment-7181 <p>What you have then is a polynomial, and any nonconstant polynomial function is unbounded.</p> Thu, 21 Jun 2012 22:53:26 +0200 Anonymous comment 7181 at http://openproblemgarden.org http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment-7162 <p> Look at sin(x)=x-x^3/6+x^5/120-....</p> <p>JPB </p> Fri, 27 Apr 2012 01:09:50 +0200 Anonymous comment 7162 at http://openproblemgarden.org http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment-6909 <p>I posted the above comment anonymously, but now I have created an account. "It seems the sum would be bounded if there are only finitely many non-zero a sub n; it is not apparent to me that a sub 0 be the only non-zero a sub n."</p> Wed, 16 Feb 2011 08:22:15 +0100 Comet comment 6909 at http://openproblemgarden.org http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment-6906 <p>It seems the sum would be bounded if there are only finitely many non-zero a sub n; it is not apparent to me that a sub 0 be the only non-zero a sub n.</p> Wed, 09 Feb 2011 23:49:10 +0100 Anonymous comment 6906 at http://openproblemgarden.org http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/rudinger_andreas">Rüdinger</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/analysis">Analysis</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Question</b>&nbsp;&nbsp; Give a necessary and sufficient criterion for the sequence <img class="teximage" src="/files/tex/0343ff13b16e6d39031bcb59a0d31a300a582fd0.png" alt="$ (a_n) $" /> so that the power series <img class="teximage" src="/files/tex/722a4892fa6950b75b1122e5f22a3459d58ec674.png" alt="$ \sum_{n=0}^{\infty} a_n x^n $" /> is bounded for all <img class="teximage" src="/files/tex/e3182ddcb88f01afefb8cee99a8319c4deb28f83.png" alt="$ x \in \mathbb{R} $" />. </div> </tr></td> </table> </td> </tr> </table> Rüdinger, Andreas boundedness power series real analysis Analysis http://openproblemgarden.org/op/criterion_for_boundedness_of_power_series#comment Sat, 09 May 2009 21:19:30 +0200 andreasruedinger 36928 at http://openproblemgarden.org