The Ramanujan Journal

, Volume 2, Issue 3, pp 387–410 | Cite as

Polynômes d'Euler et Fractions Continues de Stieltjes-Rogers

  • Dominique Dumont
  • Jiang Zeng


It is well-known that the Euler polynomials E2n(x) with n ≥ 0 can be expressed as a polynomial Hn(x(x − 1)) of x(x − 1). We extend Hn(u) to formal power series for n < 0 and prove several properties of the coefficients appearing in these polynomials or series, which generalize some recent results, independently obtained by Hammersley [7] and Horadam [8], and answer a question of Kreweras [9]. We also deduce several continued fraction expansions for the generating function of Euler polynomials, some of these formulae had been published by Stieltjes [14] and by Rogers [12] without proof. These formulae generalize our earlier results concerning Genocchi numbers, Euler numbers and Springer numbers [5, 4].

Euler polynomials Genocchi numbers continued fractions of Stieltjes-Rogers 


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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Dominique Dumont
    • 1
  • Jiang Zeng
    • 2
  1. 1.Département de MathématiqueUniversité Louis PasteurStrasbourg cédexFrance. Email
  2. 2.Institut Girard Desargues, MathématiquesUniversité Claude Bernard (Lyon I)Villeurbanne cédexFrance. Email

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