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<p>We aim to give closed integral form expressions for the extended Mathieu–type <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_986_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\({\varvec{a}}\)</EquationSource> </InlineEquation>–series and their alternating counterpart which contain an extended Gauss hypergeometric function in their summands. Additionally, we will consider a variety of particular instances and closely linked bounding inequalities.</p>

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Integral expressions and bounds for Mathieu–type \({\varvec{a}}\)-series of extended hypergeometric functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月23日

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  • Purnima Chopra,
  • Rakesh K. Parmar,
  • Tibor K. Pogány

摘要

We aim to give closed integral form expressions for the extended Mathieu–type \({\varvec{a}}\) –series and their alternating counterpart which contain an extended Gauss hypergeometric function in their summands. Additionally, we will consider a variety of particular instances and closely linked bounding inequalities.