<p>In this paper, we investigate properties of complex extension Chebyshev polynomials of the first, second, third and fourth kind, sparking interest in constructing a theory similar to the classical one. Also we consider complex (<i>p</i>,&#xa0;<i>q</i>)-extension Chebyshev wavelets on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1723_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(|x|\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>x</mi> <mo stretchy="false">|</mo> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. We define differential equation of the extension Chebyshev wavelets, and we solve the complex (<i>p</i>,&#xa0;<i>q</i>)- extension Chebyshev wavelets differential equations on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1723_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(|x|\le 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>x</mi> <mo stretchy="false">|</mo> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Complex \((p,q)-\)Extension Chebyshev Wavelets II

  • H. Mazaheri,
  • S. M. Jesmani

摘要

In this paper, we investigate properties of complex extension Chebyshev polynomials of the first, second, third and fourth kind, sparking interest in constructing a theory similar to the classical one. Also we consider complex (pq)-extension Chebyshev wavelets on \(|x|\le 1\) | x | 1 . We define differential equation of the extension Chebyshev wavelets, and we solve the complex (pq)- extension Chebyshev wavelets differential equations on \(|x|\le 1\) | x | 1 .