# On Pad\'e approximations and global relations of some Euler-type series

## TL;DR

This paper develops Padé approximations for generalized Euler-type series and uses them to analyze global relations of their p-adic values, advancing understanding of their arithmetic properties.

## Contribution

It introduces new Padé approximations for Euler-type series and applies them to study p-adic global relations, a novel approach in this context.

## Key findings

- Constructed Padé approximations of the second kind for generalized Euler series
- Applied approximations to establish global relations of p-adic values
- Enhanced understanding of the arithmetic nature of Euler-type series

## Abstract

We shall consider some special generalizations of Euler's factorial series. First we construct Pad\'e approximations of the second kind for these series. Then these approximations are applied to study global relations of certain p-adic values of the series.