2019
Том 71
№ 11

# Bodnar D. I.

Articles: 4
Article (Ukrainian)

### Multidimensional associated fractions with independent variables and multiple power series

Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 325-349

We establish the conditions of existence and uniqueness of a multidimensional associated fraction with independent variables corresponding to a given formal multiple power series and deduce explicit relations for the coefficients of this fraction. The relationship between the multidimensional associated fraction and the multidimensional $J$ -fraction with independent variables is demonstrated. The convergence of the multidimensional associated fraction with independent variables is investigated in some domains of the space $C^N$. The expansions of some functions into the corresponding two-dimensional associated fraction with independent variables are constructed and the efficiency of approaching of the obtained expansions by approximants is shown.

Article (Ukrainian)

### Corresponding branched continued fractions with linear partial numerators for double power series

Ukr. Mat. Zh. - 1991. - 43, № 4. - pp. 474-482

Article (Ukrainian)

### Pringsheim-type convergence indicators for branching continued fractions

Ukr. Mat. Zh. - 1989. - 41, № 11. - pp. 1553–1557

Article (Ukrainian)

### On the convergence of branching continued fractions with nonnegative terms

Ukr. Mat. Zh. - 1976. - 28, № 3. - pp. 373–377