Laplace contour integrals and linear differential equations
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Date
2021-07-17
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Abstract
The 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.
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Linear differential equation, Laplace contour integral, Asymptotic expansion, Order of growth, Phragmén–Lindelöf indicator, Sub-normal solution, Function of complete regular growth, Distribution of zeros