<p>In the paper, we explored the growth properties of solutions of the complex linear differential equations characterised by meromorphic or analytic coefficients of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_888_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left[ p,q\right] \)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="]" open="["> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mfenced> </math></EquationSource> </InlineEquation>-order near a singular point, where <i>p</i> and <i>q</i> are positive integers with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_888_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\ge q\ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>≥</mo> <mi>q</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. Furthermore, we have introduced several new findings that enhance and expand upon previous research outcomes.</p>

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On the growth of solutions to complex linear differential equations near a singular point

  • Samten Tamang,
  • Tanushree Roy

摘要

In the paper, we explored the growth properties of solutions of the complex linear differential equations characterised by meromorphic or analytic coefficients of \(\left[ p,q\right] \) p , q -order near a singular point, where p and q are positive integers with \(p\ge q\ge 1\) p q 1 . Furthermore, we have introduced several new findings that enhance and expand upon previous research outcomes.