Volterra chain and Catalan numbers
classification
🌊 nlin.SI
math.CO
keywords
catalanchainnumbersproblemvolterraadmitsarisingbessel
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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 Catalan numbers.
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