Skip to main content
SpringerLink
Log in

Kapteyn series and photon emission

  • Published:
Bulletin of the Lebedev Physics Institute Aims and scope Submit manuscript

Abstract

Sums of Kapteyn series of several types are obtained and relations between them are found. Special attention is paid to series whose sums are expressed in terms of transcendent functions. Their asymptotics are determined. In some cases, integral representations were obtained and reduced to the form convenient for numerical calculations. The electron lifetime in a constant electromagnetic field before photon emission is determined. It was indicated that this time increases with the ultrarelativistic electron energy in a strong constant field.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. I. Nikishov, arXiv:1.302.0978 [math.ph] 5 Feb 2013.

  2. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965; Nauka, Moscow, 1979).

    Google Scholar 

  3. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Series and Products (Fizmatlit, Moscow, 1963) [in Russian].

    Google Scholar 

  4. G. N. Watson, A Treaty on the Theory of Bessel Functions (Cambridge Univ. Press, Cambridge, 1966).

    Google Scholar 

  5. G. A. Schott, Electromagnetic Radiation (Cambridge Univ. Press, Cambridge, 1912).

    MATH  Google Scholar 

  6. D. D. Ivanenko and A. A. Sokolov, Classical Field Theory (Gostekhizdat, Moscow, 1951) [in Russian].

    Google Scholar 

  7. L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, Moscow, 1973; Oxford, Pergamon 1977).

    Google Scholar 

  8. A. I. Nikishov and V. I. Ritus, Zh. Eksp. Teor.Fiz. 46, 776 (1964).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991, Russia

    A. I. Nikishov

Authors
  1. A. I. Nikishov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Nikishov.

Additional information

Original Russian Text © A.I. Nikishov, 2014, published in Kratkie Soobshcheniya po Fizike, 2014, Vol. 41, No. 11, pp. 43–51.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nikishov, A.I. Kapteyn series and photon emission. Bull. Lebedev Phys. Inst. 41, 332–338 (2014). https://doi.org/10.3103/S1068335614110062

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068335614110062

Keywords

Search

Navigation