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Mathematik-Online problems:

Problem 129: Binomial Series

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
For $ \alpha\in\mathbb{R}$ and $ n\in\mathbb{N}_0$ the binomial coefficient $ \left(\alpha\atop n\right)$ is defined by

$\displaystyle \left(\!\begin{array}{c}\alpha\\ n\end{array}\!\right)\,:=\,\frac{\alpha\,(\alpha-1)(\alpha-2)\cdots (\alpha-n+1)}{n!}\,. $

Find the radius of convergence of the binomial series $ {\displaystyle{\sum_{n=0}^\infty \left(\!\begin{array}{c}\alpha\\ n\end{array}\!\right) x^n}}$
a)
for the case $ \alpha\in\mathbb{R}\setminus\mathbb{N}_0$
b)
for the case $ \alpha\in\mathbb{N}_0$

(Authors: /Höfert)

Solution:

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  automatisch erstellt am 14. 10. 2004