# A new class of special functions arising from the solution of differential equations involving multiple proportional delays

## TL;DR

This paper introduces a new class of special functions derived from differential equations with multiple proportional delays, expanding the landscape of special functions with unique properties and identities.

## Contribution

It presents a novel class of special functions arising from differential equations with multiple proportional delays, which are independent of existing special functions.

## Key findings

- New class of special functions identified
- Basic properties and identities analyzed
- Independence from existing special functions established

## Abstract

Proportional delay is a particular case of time dependent delay. In this article, we consider differential equations involving multiple delays. The series solution of this equation leads to a class of special functions. This class of special functions is independent from all the existing special functions obtained as a solution of differential equations. We analyze the basic properties of this class and discuss various identities and relations.