Il Nuovo Cimento B (1971-1996)

, Volume 107, Issue 4, pp 443–452 | Cite as

Transformations between two normal differential equations. Application to the bessel functions

  • R. Pons
  • B. Léauté
  • G. Marcilhacy


We extend Chandrasekhar’s black-hole transformation which concerns the transformation between two normal linear differential equations. We use the properties of the corresponding Riccati’s equations and of Schwarzian’s derivative to find a new correspondence between these normal equations.

PACS 02.30.Hq

Ordinary differential equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    F. J. Zerilli:Phys. Rev. D,2, 214 (1970).MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    J. M. Bardeen andW. H. Press:J. Math. Phys.,14, 7 (1973).MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    T. Regge andJ. A. Wheeler:Phys. Rev.,108, 1063 (1957).MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    S. Chandrasekhar:The Mathematical Theory of Black Holes, Intern. Series of Monogr. Phys. (Oxford, 1963).Google Scholar
  5. [5]
    J. Heading:J. Phys. A,10, 885 (1977).MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    J. Heading:Proc. R. Soc. Edinburgh, Sect. A,79, 87 (1977).MathSciNetGoogle Scholar
  7. [7]
    E. Hille:Ordinary Differential Equations in the Complex Domain (John Wiley & Sons, New York, N. Y., 1976).Google Scholar
  8. [8]
    G. Petiau:La théorie des fonctions de Bessel (C.N.R.S., Paris, 1955).Google Scholar

Copyright information

© Società Italiana di Fisica 1992

Authors and Affiliations

  • R. Pons
    • 1
  • B. Léauté
    • 2
  • G. Marcilhacy
    • 2
  1. 1.Physique Mathématique des PlasmasUniversité P. et M. CurieParis Cedex 05France
  2. 2.URA au C.N.R.S. n° 769, Université P. et M. CurieInstitut Henri PoincaréParis Cedex 05France

Personalised recommendations