Steinmetz, Norbert2022-03-072022-03-072021-07-17http://hdl.handle.net/2003/40769http://dx.doi.org/10.17877/DE290R-22626The purpose of this paper is to determine the main properties of Laplace contour integrals Λ(z)=12πi∫Cϕ(t)e−ztdt that solve linear differential equations L[w](z):=w(n)+∑j=0n−1(aj+bjz)w(j)=0. This concerns, in particular, the order of growth, asymptotic expansions, the Phragmén–Lindelöf indicator, the distribution of zeros, the existence of sub-normal and polynomial solutions, and the corresponding Nevanlinna functions.enLinear differential equationLaplace contour integralAsymptotic expansionOrder of growthPhragmén–Lindelöf indicatorSub-normal solutionFunction of complete regular growthDistribution of zeros520Text