http://ask.metafilter.com/tags/coefficients Questions tagged with 'coefficients' at Ask MetaFilter. Tue, 27 Nov 2007 07:23:17 -0800 Tue, 27 Nov 2007 07:23:17 -0800 en-us http://blogs.law.harvard.edu/tech/rss 60 http://ask.metafilter.com/77206/Whats%2Dthe%2Dnext%2Dpolynomial%2Din%2Dthis%2Dseries What's the next polynomial in this series: x⁴+2x²+16, x⁸+40x⁶+1128x⁴+2560x²+65536, ? I'm doing some work in elasticity and have found an analytical solution to a tricky problem. The solution is a converging infinite series, and I've been able to work out the first two terms (with great difficulty). It may be easier to guess the additional terms than work them out. The next polynomial almost certainly has seven terms, including x¹² and 2,176,782,336 (6¹²). Any guesses as to what the other coefficients are, and what the general pattern is?<br> <br> (The sum converges because the denominators are (4+x²)^5/2, (16+x²)^9/2, ... and every other term is subtracted.) tag:ask.metafilter.com,2007:site.77206 Tue, 27 Nov 2007 07:23:17 -0800 coefficients converge infinite polynomials series sum Mapes