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<p>This paper studies the strong starlikeness of analytic functions associated with the right-half plane Cassini oval by establishing coefficient conditions for their power series expansions. The study utilizes the Cauchy product of power series along with key inequalities involving the Pochhammer symbol and the Gamma function. A special case of the main result leads to the lemniscate starlikeness of analytic functions. The derived results are further applied to several special functions, providing parameter restrictions under which these functions become strongly starlike and hence lemniscate starlike. The findings extend and refine several earlier results in this domain.</p>

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On the starlikeness of analytic functions associated with Cassini oval with applications to special functions

  • 期刊论文

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  • 发表日期：

    2026年5月20日

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  • Saiful R Mondal,
  • Ahmad K. Al Abdulaali

摘要

This paper studies the strong starlikeness of analytic functions associated with the right-half plane Cassini oval by establishing coefficient conditions for their power series expansions. The study utilizes the Cauchy product of power series along with key inequalities involving the Pochhammer symbol and the Gamma function. A special case of the main result leads to the lemniscate starlikeness of analytic functions. The derived results are further applied to several special functions, providing parameter restrictions under which these functions become strongly starlike and hence lemniscate starlike. The findings extend and refine several earlier results in this domain.