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3 results

  • Bounds for modified Bessel functions of the first and second kinds

  • Árpád Baricz
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 53 / Issue 3 / October 2010
    Published online by Cambridge University Press:
    05 August 2010, pp. 575-599
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  • Some new inequalities for quotients of modified Bessel functions of the first and second kinds are deduced. Moreover, some developments on bounds for modified Bessel functions of the first and second kinds, higher-order monotonicity properties of these functions and applications to a special function that arises in finite elasticity, are summarized. The key tool in our proofs is a frequently used criterion for the monotonicity of the quotient of two Maclaurin series.

  • TURÁN TYPE INEQUALITIES FOR MODIFIED BESSEL FUNCTIONS

  • ÁRPÁD BARICZ
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 82 / Issue 2 / October 2010
    Published online by Cambridge University Press:
    07 April 2010, pp. 254-264
    Print publication:
    October 2010
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  • In this paper our aim is to deduce some sharp Turán type inequalities for modified Bessel functions of the first and second kinds. Our proofs are based on explicit formulas for the Turánians of the modified Bessel functions of the first and second kinds and on a formula which is related to the infinite divisibility of the Student t-distribution.

  • INCOMPLETE BESSEL FUNCTIONS. II. ASYMPTOTIC EXPANSIONS FOR LARGE ARGUMENT

  • D. S. Jones
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 50 / Issue 3 / October 2007
    Published online by Cambridge University Press:
    08 January 2008, pp. 711-723
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  • Asymptotic expansions for an incomplete Bessel function of large argument are derived when the parametric point (a) is well away from any saddle point, (b) coincides with a saddle point and (c) is in the neighbourhood of a saddle point.