×

zbMATH — the first resource for mathematics

Integrated version of the Post-Widder inversion formula for Laplace transforms. (English) Zbl 1236.44003
The formula mentioned in the title reads \[ f(t)= \lim_{n\to\infty}(-1)^n/(n!\Gamma(\alpha))\int^t_0 (t-s)^{\alpha-1} (n/s)^{n+1}(d^n/d\lambda^n)(\lambda^\alpha\widehat f(\lambda))|_{\lambda= n/s}\,ds, \] where \(\widehat f\) is the Laplace transform of the vector-valued function \(f\). The result is applied to \(\alpha\)-times integrated semigroups resp. cosine functions.
MSC:
44A10 Laplace transform
47D62 Integrated semigroups
44A20 Integral transforms of special functions
PDF BibTeX XML Cite
Full Text: DOI