Limit of x^a log(x)=0
From specialfunctionswiki
Theorem
The following formula holds for $a \in \mathbb{C}$ with $\mathrm{Re}(a)>0$: $$\displaystyle\lim_{x \rightarrow 0^+} x^a \log(x)=0,$$ where $\log$ denotes the logarithm.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $4.1.31$
