From the cosine integral (int cos (omega t) e^{-|omega|^{alpha}} d omega), deduce that the (alpha)-stable density has
Question:
From the cosine integral \(\int \cos (\omega t) e^{-|\omega|^{\alpha}} d \omega\), deduce that the \(\alpha\)-stable density has a Taylor series at the origin which begins
\[
\log p(t ; 1 / 2)=\text { const }-60 t^{2}+O\left(t^{4}ight) \text {. }
\]
Find the general term in this expansion and deduce the radius of convergence.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: