Abstract
In this paper, the Poincaré-Bertrand formula for the fractional Hilbert
transform is derived using properties of Chebyshev polynomial functions.
This formula finds applications in various fields where singular
integral equations with Cauchy kernels are prevalent. The formula allows
for changing the order of integration when both integrals involve a
Cauchy’s principal value. This paper presents a detailed derivation and
proof of the Poincaré-Bertrand formula for fractional Hilbert transform.
This formula is significant in various fields, including signal
processing, image processing, and mathematical physics.