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New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean

Author

Listed:
  • Ling Zhu

    (Department of Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China)

Abstract

Let I p x be the modified Bessel function of the first kind of order p . The upper and lower bounds in the form of simple rational functions about cosh t and ( sinh t ) / t for the function I 0 x are obtained. The corresponding inequalities for the Toader-Qi mean do not match those in the existing literature.

Suggested Citation

  • Ling Zhu, 2021. "New Bounds for the Modified Bessel Function of the First Kind and Toader-Qi Mean," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2867-:d:676889
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