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On application of Euler’s differential method to a continued fraction depending on parameter

Author

Listed:
  • Agamirza E. Bashirov

    (Eastern Mediterranean University)

  • Mahmoud Jafari Shah Belaghi

    (Bahcesehir University)

Abstract

In this paper we apply Euler’s differential method, which was not used by mathematicians for a long time, to derive a new formula for a certain kind irregular continued fraction depending on a parameter. This formula is in the form of the ratio of two integrals. In case of integer values of the parameter, the formula reduces to the ratio of two finite sums. Asymptotic behavior of this continued fraction is investigated numerically and it is shown that it increases in the same rate as the root function.

Suggested Citation

  • Agamirza E. Bashirov & Mahmoud Jafari Shah Belaghi, 2014. "On application of Euler’s differential method to a continued fraction depending on parameter," Indian Journal of Pure and Applied Mathematics, Springer, vol. 45(3), pages 285-296, June.
    • Handle: RePEc:spr:indpam:v:45:y:2014:i:3:d:10.1007_s13226-014-0063-x
    DOI: 10.1007/s13226-014-0063-x
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