Skip to main content

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
Cancel
×
×
Home
  • Home
Article
  • Cited by 4
  • Cited by
    Crossref Citations
    Crossref logo
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.
    Kerimov, M. K. 2016. Studies on the zeros of Bessel functions and methods for their computation: 2. Monotonicity, convexity, concavity, and other properties. Computational Mathematics and Mathematical Physics, Vol. 56, Issue. 7, p. 1175.
    Ifantis, E.K. and Siafarikas, P.D. 1992. A differential inequality for the positive zeros of Bessel functions. Journal of Computational and Applied Mathematics, Vol. 44, Issue. 1, p. 115.
    Colton, D. Ifaktis, E. K. and Siafarikas, P. D. 1985. An Inequality Related the Zeros of Two Ordinary Bessel Functions. Applicable Analysis, Vol. 19, Issue. 4, p. 251.
    Ifantis, E.K. and Siafarikas, P.D. 1985. A differential equation for the zeros of bessel functions. Applicable Analysis, Vol. 20, Issue. 3-4, p. 269.
    ×
  • Access

Monotonicity properties of the zeros of Bessel functions

  • Roger C. McCann and E. R. Love
Abstract

Let jν, denote the first positive zero of Jν. It is shown that jν/(ν + α) is a strictly decreasing function of ν for each positive α provided ν is sufficiently large. For each α lowe bounds on ν are given to assure the monotonicity of jν/(ν + α). From this it is shown that jν > ν + j0 for all ν > 0, which is both simpler and an improvement on the well known inequality Jν ≥ (ν (ν + 2))1/2.

    •
      • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Monotonicity properties of the zeros of Bessel functions
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Monotonicity properties of the zeros of Bessel functions
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Monotonicity properties of the zeros of Bessel functions
      Available formats
      ×
Copyright
COPYRIGHT: © Australian Mathematical Society 1982
References
Hide All
[1]Abramowitz, M. and Stegun, I. A. (eds.), Handbook of mathematical funcrions (Dover, New York, 1970).
[2]Courant, R. and Hilbert, D., Methods of mathematical physics, Vol.1 (Interscience, New York, 1953).
[3]Gray, A., Mathews, G. B. and MacRobert, T. M., A treatise on the theory of Bessel functions (2nd edition, Dover, New York, 1966).
[4]Hethcote, H. W., “Error bounds for asymptotic approximations to zeros of transcendental functions”, SIAM J. Math. Anal. 1 (1970), 147–152.
[5]Jahnke, E. and Emde, F., Tables of functions (4th edition, Dover, New York, 1945).
[6]Lewis, J. T. and Muldoon, M. E., “Monotonicity and convexity properties of zeros of Bessel functions”, SIAM J. Math. Anal. 8 (1977), 171–178.
[7]Luke, Y. L., Integrals of Bessel functions (McGraw-Hill, New York, 1962).
[8]McCann, R. C., “Inequalities for the zeros of Bessel functions”, SIAM J. Math. Anal. 8 (1977), 166–170.
[9]McCann, R. C., “Lower bounds for the zeros of Bessel functions”, Proc. Amer. Math. Soc. 64 (1977), 101–103.
[10]Mikhlin, S. G., Variational methods of mathematical physics (Macmillan, New York, 1964).
[11] National Bureau of Standards, Tables of spherical Bessel functions, Vol. 2 (Columbia University Press, New York, 1950).
[12]Olver, F. W. J., (ed), Royal society mathematical tables, Vol. 7, Bessel functions, Part III, Zeros and associated values (Cambridge University Press, Cambridge, 1960).
[13]Royden, H. L., Real analysis (Macmillan, New York, 1963).
[14]Tricomi, F. G., “Sulle funzioni di Bessel di ordine e argomento pressoché uguale”, Atti. Accad. Sci. Torino Cl. Sci. Fis. Mat. Nat. 83 (1949), 3–20.
[15]Watson, G. N., A treatise on the theory of Bessel functions (Cambridge University Press, 2nd edition, Cambridge, 1945).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The ANZIAM Journal
  • ISSN: 1446-1811
  • EISSN: 1446-8735
  • URL: /core/journals/anziam-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

CAPTCHA *

Skip to the audio challenge
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 35 *
Loading metrics...

Abstract views

Total abstract views: 31 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 13th June 2018. This data will be updated every 24 hours.

Cancel
Confirm
×