Generalised definitions of certain functions and their uses

TL;DR

This paper introduces generalized versions of exponential, sine, cosine, hyperbolic sine, and hyperbolic cosine functions, exploring their properties and potential applications beyond classical functions.

Contribution

It provides new generalized definitions of key functions and discusses their properties and significance for future mathematical applications.

Findings

Generalized functions extend classical exponential and trigonometric functions.

Properties of these functions are systematically analyzed.

Potential applications in various mathematical and scientific fields are considered.

Abstract

Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the properties of the generalised functions are discussed. Importance of these functions and their possible applications are also considered.