Finite Integral Involving Incomplete Aleph-functions and Fresnel Integral

Document Type : Regular research papers


1 Mathematics Department, Asst. Professor, St. Mary's PG College, Vidisha, India

2 St. Mary's PG College, Vidisha (MP)

3 College Jean L’herminier, Alleedes Nympheas, 83500 La Seyne-sur-Mer, FRANCE


Special functions represent a class of mathematical functions that have
achieved a distinct and recognized status within the realms of mathematical analysis,
functional analysis, geometry, physics, and diverse practical applications. These
functions have emerged as notable tools in these disciplines, owing to their unique
properties and inherent significance. Over time, they have become firmly established
due to their ability to address specific mathematical challenges and contribute valuable
insights to various branches of science and engineering. The primary objective of this
paper is to establish a thorough definition of comprehensive finite integrals through the
incorporation of both the Fresnel integral and incomplete Aleph-functions. By adopting
a unified and general approach, these integrals are shown to yield a diverse range
of new outcomes, particularly in specific scenarios. To elucidate and underscore the
significance of our contributions, we present a detailed exposition of our findings, accompanied
by specific corollaries. These corollaries, in turn, are emphasized as special
cases derived directly from the fundamental results outlined in our study.


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