Alexander Lyapin
@sfu-kras.ru
Mathematics and Computer Science
Siberian Federal University
RESEARCH, TEACHING, or OTHER INTERESTS
Mathematics
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Svetlana S. Akhtamova, Tom Cuchta, and Alexander P. Lyapin
MDPI AG
We extend existing functional relationships for the discrete generating series associated with a single-variable linear polynomial coefficient difference equation to the multivariable case.
S. S. Akhtamova, V. S. Alekseev, and A. P. Lyapin
Pleiades Publishing Ltd
M. S. Apanovich, A. P. Lyapin, and K. V. Shadrin
Pleiades Publishing Ltd
A. P. Lyapin and E. N. Mikhalkin
Pleiades Publishing Ltd
M. S. Apanovich, A. P. Lyapin, and K. V. Shadrin
Pleiades Publishing Ltd
A. P. Lyapin, , T. Tom, , and
Irkutsk State University
We consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lattice <math xmlns='http://www.w3.org/1998/Math/MathML'><msup><mi>Z</mi><mi>n</mi></msup></math> to find a recurrence relation (difference equation with polynomial coefficients) for the section of the generating series. This formula allows us to find a generating series of a solution to the Cauchy problem in the lattice cone through a generating series of its initial data and a right-side function of the difference equation. We derived an integral representation for sections of the holomorphic function, whose coefficients satisfy the difference equation with complex coefficients. Finally, we propose a system of differential equations for sections that represent D-finite functions of two complex variables.
A.P. Lyapin and S.S. Akhtamova
Udmurt State University
In this paper, we study the sections of the generating series for solutions to a linear multidimensional difference equation with constant coefficients and find recurrent relations for these sections. As a consequence, a multidimensional analogue of Moivre's theorem on the rationality of sections of the generating series depending on the form of the initial data of the Cauchy problem for a multidimensional difference equation is proved. For problems on the number of paths on an integer lattice, it is shown that the sections of their generating series represent the well-known sequences of polynomials (Fibonacci, Pell, etc.) with a suitable choice of steps.
M. S. Apanovich, A. P. Lyapin, and K. V. Shadrin
Pleiades Publishing Ltd
Alexander P. Lyapin and Sreelatha Chandragiri
Informa UK Limited
ABSTRACT We define a generalized vector partition function and derive an identity for the generating series of such functions associated with solutions to basic recurrence relations of combinatorial analysis. As a consequence we obtain the generating function of the number of generalized lattice paths and a new version of the Chaundy-Bullard identity for the vector partition function.
A. A. Kytmanov, A. P. Lyapin, and T. M. Sadykov
Pleiades Publishing Ltd