2019/07/31 by Dirk Veestraeten, Veestraeten, Dirk
Mathematics · #33B20 #33C05 #33C15 #33C20 #44A10 #44A35 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1908.00001
openalex publication_date 2019/07/31 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
This paper uses the convolution theorem of the Laplace transform to derive\nnew inverse Laplace transforms for the product of two parabolic cylinder\nfunctions in which the arguments may have opposite sign. These transforms are\nsubsequently specialized for products of the error function and its complement\nthereby yielding new integral representations for products of the latter two\nfunctions. The transforms that are derived in this paper also allow to correct\ntwo inverse Laplace transforms that are widely reported in the literature and\nsubsequently uses one of the corrected expressions to obtain two new definite\nintegrals for the generalized hypergeometric function.\n