# On polynomials of binomial type, Ramanujan-Soldner constant and inverse logarithmic derivative operator

## TL;DR

This paper explores properties of polynomials of binomial type, introduces new series related to the Ramanujan-Soldner constant, and studies the inverse logarithmic derivative operator using Lagrange inversion.

## Contribution

It introduces new infinite series connected to the Ramanujan-Soldner constant and analyzes the inverse logarithmic derivative operator within the framework of polynomials of binomial type.

## Key findings

- New series related to Ramanujan-Soldner constant
- Properties of the 1/dlog operator on formal power series
- Characterization of polynomials of binomial type linked to elementary functions

## Abstract

In this work we introduce interesting infinite series, related to Ramanujan-Soldner constant. Our method uses general properties of polynomials of binomial type and Lagrange inversion theorem. Also we study properties of the operator 1/dlog, acting on formal power series. In addition, several properties of polynomials of binomial type associated to elementary functions are discussed.