On irrational values of the error function and gamma function

TL;DR

This paper explores the irrationality of certain mathematical constants related to the error and gamma functions, building on Ramanujan's work with infinite series and continued fractions.

Contribution

It introduces a recursive formula to demonstrate the irrationality of specific open problems involving the error and gamma functions, extending Ramanujan's classical results.

Findings

Established irrationality of certain values related to the error function

Developed a recursive method for analyzing irrationality of mathematical constants

Connected classical Ramanujan series to modern irrationality proofs

Abstract

In this paper, we establish the irrationality of some open problems in mathematics based on using a recursive formula that generate the complete sequence of numbers. see [1] But before getting into that we begin with some Ramanujan notable work of infinite series and continued fraction.