Skip to main content
SpringerLink
Log in

Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero

  • Ordinary Differential Equations
  • Published:
Differential Equations Aims and scope Submit manuscript

Abstract

We specify the structure of the power series determining a solution of a Fuchsian second-order differential equation with polynomial coefficients in a neighborhood of zero. The power series is represented via hypergeometric functions of fractional order. The structure of the coefficients of the series is clarified.

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. Ince, E.L., Ordinary Differential Equations, London, 1926. Translated under the title Obyknovennye differentsial’nye uravneniya, Kharkov, 1939.

  2. Golubev, V.V., Lektsii po analiticheskoi teorii differentsial’nykh uravnenii (Lectures on the Analytic Theory of Differential Equations), Moscow: Gosudarstv. Izdat. Tekhn.-Teor. Lit., 1950.

    Google Scholar 

  3. Slavyanov, S.Yu. and Lai, V., Spetsial’nye funktsii. Edinaya teoriya, osnovannaya na analize osobennostei (Special Functions. Unified Theory Based on Analysis of Singularities), St. Petersburg, 2002.

  4. Wimp, J., Computation with Recurrence Relations, Boston, 1984.

  5. Sansone, G., Equazioni differenziali nel campo reale. Pt. 1, Bologna, 1948. Translated under the title Obyknovennye differentsial’nye uravneniya. T. 1, Moscow: Inostrannay Literatura, 1953.

  6. Kruglov, V.E., Solution of a Second-Order Equation of Poincaré-Perron Type and the Differential Equations That Can Be Reduced to It, Ukrain. Mat. Zh., 2008, vol. 60, no. 7, pp. 900–917.

    MathSciNet  MATH  Google Scholar 

  7. Kruglov, V.E., Closed-Form Solution of a Second-Order Differential Equation with Finitely Many Singular Points, in Tez. Mizhnar. konf. im. V.Ya. Skorobogat’ka (Abstr. V.Ya. Skorobogat’ka Int. Conf.), Dorogobich, 2007, p. 151.

  8. Vilenkin, N.Ya., Kombinatorika (Combinatorics), Moscow: Nauka, 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Odessa National University, Odessa, Ukraine

    V. E. Kruglov

Authors
  1. V. E. Kruglov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.E. Kruglov, 2011, published in Differentsial’nye Uravneniya, 2011, Vol. 47, No. 1, pp. 21–28.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kruglov, V.E. Solution of a second-order linear differential equation with polynomial coefficients and Fuchsian point at zero. Diff Equat 47, 20–28 (2011). https://doi.org/10.1134/S0012266111010034

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0012266111010034

Keywords

Search

Navigation