most recent 30 from http://mathoverflow.net 2013-05-19T22:09:26Z http://mathoverflow.net/feeds/question/85380 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/85380/finite-sum-of-modified-bessel-function-of-the-second-type Remy 2012-01-11T01:32:39Z 2012-01-11T01:32:39Z

<p>I have a sum of the form</p> <p>$\sum^n_{i=0} \frac{{t}^{i} z^{i}}{i!}K_{a+i}(z), \quad\quad z\in\mathbb{R},z>0$</p> <p>where $K$ is the modified Bessel function of the second type and $a$ is an integer, $t\in\mathbb{R}$ and $t>0$. </p> <p>I know that if the sum is infinite, this can be solved using the multiplication theorem, but any hints for solving the finite case?</p>