3 papers
nlin.SI2010
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
Paul E. Spicer, Frank W. Nijhoff, Peter H. van der Kamp
The discrete-time Toda equation arises as a universal equation for the relevant Hankel determinants associated with one-variable orthogonal polynomials through the mechanism of adj…
nlin.SI2009
Semi-classical Laguerre polynomials and a third order discrete integrable equation
P. E. Spicer, F. W. Nijhoff
A semi-discrete Lax pair formed from the differential system and recurrence relation for semi-classical orthogonal polynomials, leads to a discrete integrable equation for a specif…
nlin.SI2009
Direct delay reductions of the Toda hierarchy
Nalini Joshi, Paul E. Spicer
We apply the direct method of obtaining reductions to the Toda hierarchy of equations. The resulting equations form a hierarchy of ordinary differential difference equations, also…