arXiv subjects
Publications and source records attributed to Emin Özçağ.
In this paper the incomplete gamma function $γ(α,x)$ and its derivative is considered for negative values of $α$ and the incomplete gamma type function $γ_*(α,x_-)$ is introduced. Further the polygamma functions $ψ^{(n)}(x)$ are defined for negative integers via the neutrix setting.
In this paper we define the polygamma functions $ψ^{(n)}(x)$ for negative integers by using neutrix calculus.
The Lax type integrability of a two-component polynomial Burgers type dynamical system within a differential-algebraic approach is studied, its linear adjoint matrix Lax representation is constructed. A related recursion operator and infnite hierarchy of Lax integrable nonlinear dynamical systems of the Burgers-Korteweg-de Vries type are derived by means of the gradient-holonomic technique, the corresponding Lax type representations are presented.
There is developed a differential-algebraic approach to studying the representations of commuting differentiations in functional differential rings under nonlinear differential constraints. An example of the differential ideal with the only one conserved quantity is analyzed in detail, the corresponding Lax type representations of differentiations are constructed for an infinite hierarchy of nonlinear dynamical systems of the Burgers and Korteweg-de Vries type. A related infinite bi-Hamiltonian hierarchy of Lax type dynamical systems is constructed.