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Volterra Chain and Catalan Numbers

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Abstract

We consider the Cauchy problem for the Volterra chain with an initial condition equal to 0 in one node and 1 in the others. It is shown that this problem admits an exact solution in terms of the Bessel functions. The Taylor series arising here are related to the exponential generating function for the Catalan numbers.

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References

  1. R. Ch. Kulaev and A. B. Shabat, Ufa Math. J. (2018, accepted).

    Google Scholar 

  2. N. J. A. Sloane, http://oeis.org (2010).

    Google Scholar 

  3. J. W. Layman, J. Integer Seq. 4, 01.1.5 (2001).

    Google Scholar 

  4. Y. Kodama and V. U. Pierce, Comm. Math. Phys. 292, 529 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  5. A. N. Leznov, Theor. Math. Phys. 42, 225 (1980).

    Article  Google Scholar 

  6. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas (Dover, New York, 1972).

    MATH  Google Scholar 

  7. O. I. Bogoyavlensky, Russ. Math. Surv. 46 (3), 1 (1991).

    Article  Google Scholar 

  8. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics (Addison-Wesley, Reading, MA, 1990).

    MATH  Google Scholar 

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Correspondence to V. E. Adler.

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Published in Russian in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2018, Vol. 108, No. 12, pp. 834–837.

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Adler, V.E., Shabat, A.B. Volterra Chain and Catalan Numbers. Jetp Lett. 108, 825–828 (2018). https://doi.org/10.1134/S0021364018240013

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  • DOI: https://doi.org/10.1134/S0021364018240013