# A Note on d-Hankel Transforms, Continued Fractions, and Riordan Arrays

## TL;DR

This paper extends the Hankel transform to multiple sequences, exploring its connections to generalized continued fractions and $d$-orthogonal sequences, thereby broadening the mathematical framework for analyzing complex integer sequences.

## Contribution

It introduces a natural extension of the Hankel transform to $d$-sequences and investigates its relationship with generalized continued fractions and $d$-orthogonal sequences.

## Key findings

- Extended Hankel transform to $d$-sequences.
- Linked $d$-Hankel transforms to generalized continued fractions.
- Provided new insights into $d$-orthogonal sequences.

## Abstract

The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued fractions in the context of $d$-orthogonal sequences.