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arXiv · 2009.07550

Laplace contour integrals and linear differential equations

Norbert Steinmetz
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Abstract

The purpose of this paper is to determine the main properties of Laplace contour integrals $$\Lambda(z)=\frac1{2\pi i}\int_\CC\phi_L(t)e^{-zt}\,dt,$$ that solve linear differential equations $$L[w](z):=w^{(n)}+\sum_{j=0}^{n-1}(a_j+b_jz)w^{(j)}=0.$$ This concerns, in particular, the order of growth, asymptotic expansions, the Phragm\'en-Lindel\"of indicator, the distribution of zeros, the existence of sub-normal and polynomial solutions, and the corresponding Nevanlinna functions.

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Norbert Steinmetz. 2020-09-16. Laplace contour integrals and linear differential equations. https://arxiv.org/abs/2009.07550

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