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<p>The paper is devoted to the study of a six-parameter generalization of the Krätzel function introduced by E. Krätzel [Integral transformations of Bessel type, in Generalized Functions and Operational Calculus, Bulgarian Academy of Sciences, Sofia, 1979, pp.<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( 148-155 \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>148</mn> <mo>-</mo> <mn>155</mn> </mrow> </math></EquationSource> </InlineEquation>]. The representation of the function in terms of a series and an <i>H</i>-function is presented. The analytic properties like log-convexity, complete monotonicity and Turán type inequality of the function are substantiated. Furthermore, the concordance of the dual pathway generalized Krätzel function with the Weyl fractional integral and differential operators is examined.</p>

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On dual pathway generalized Krätzel function

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Dilip Kumar,
  • Ajina S. Ajai

摘要

The paper is devoted to the study of a six-parameter generalization of the Krätzel function introduced by E. Krätzel [Integral transformations of Bessel type, in Generalized Functions and Operational Calculus, Bulgarian Academy of Sciences, Sofia, 1979, pp. \( 148-155 \) 148 - 155 ]. The representation of the function in terms of a series and an H-function is presented. The analytic properties like log-convexity, complete monotonicity and Turán type inequality of the function are substantiated. Furthermore, the concordance of the dual pathway generalized Krätzel function with the Weyl fractional integral and differential operators is examined.