### Abstract

Using the notion of composita and the Lagrange inversion theorem, we present techniques for solving the following functional equation B(x)=H(xB(x)^{m}), where H(x),B(x) are generating functions and m ∈ N. Also we give some examples.

Original language | English |
---|---|

Journal | Advances in Difference Equations |

Volume | 2015 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- composita
- functional equation
- generating function
- Lagrange inversion theorem

### ASJC Scopus subject areas

- Applied Mathematics
- Algebra and Number Theory
- Analysis

### Cite this

*Advances in Difference Equations*,

*2015*(1). https://doi.org/10.1186/s13662-014-0347-9

**On solving some functional equations.** / Kruchinin, Dmitry V.

Research output: Contribution to journal › Article

*Advances in Difference Equations*, vol. 2015, no. 1. https://doi.org/10.1186/s13662-014-0347-9

}

TY - JOUR

T1 - On solving some functional equations

AU - Kruchinin, Dmitry V.

PY - 2015

Y1 - 2015

N2 - Using the notion of composita and the Lagrange inversion theorem, we present techniques for solving the following functional equation B(x)=H(xB(x)m), where H(x),B(x) are generating functions and m ∈ N. Also we give some examples.

AB - Using the notion of composita and the Lagrange inversion theorem, we present techniques for solving the following functional equation B(x)=H(xB(x)m), where H(x),B(x) are generating functions and m ∈ N. Also we give some examples.

KW - composita

KW - functional equation

KW - generating function

KW - Lagrange inversion theorem

UR - http://www.scopus.com/inward/record.url?scp=84922041656&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84922041656&partnerID=8YFLogxK

U2 - 10.1186/s13662-014-0347-9

DO - 10.1186/s13662-014-0347-9

M3 - Article

VL - 2015

JO - Advances in Difference Equations

JF - Advances in Difference Equations

SN - 1687-1839

IS - 1

ER -