arXiv subjects

Snehasis Bera

Publications and source records attributed to Snehasis Bera.

4 recordsLinked to original sources

arXiv2026

A new class of coherent states involving Fox-Wright functions and their generalization in the bicomplex framework

In this work, an extensive class of coherent states is introduced by taking the Fox Wright function as the normalization function. It is demonstrated that these states satisfy the key requirements of continuity, normalizability and resolution of unity. Furthermore, coherent states associated with the continuous spectrum are obtained through a discrete to continuous limiting procedure. Moreover, FW generalized multi parameter nu function is introduced and shown to act as the normalization function for the Fox Wright coherent states in the continuous spectrum. Later the Fox Wright function with bicomplex arguments has been introduced and its existence has been investigated. Bicomplex Fox Wright coherent states are also developed for the discrete spectrum based on this new function and their properties are analyzed. Subsequently, the results regarding Fox Wright coherent states are generalized to the bicomplex setting. In addition, a bicomplex FW generalized multi-parameter nu function is defined to demonstrate that it provides the normalization for these states in the continuous spectrum.

quant-ph↗

arXiv2025

On the Bessel function and $n$-dimensional Hankel transform with Bicomplex arguments and coherent states

In this work, we introduce bicomplex Bessel function and analyze its region of convergence. Important properties of the bicomplex Bessel function, such as recurrence relations, integral representations, differential relations are explored. Moreover a differential equation satisfied by the bicomplex Bessel function is established. Furthermore, we investigate bicomplex holomorphicity and discuss its asymptotic behavior. Finally, we define $n$-dimensional bicomplex Hankel transformation by using bicomplex Bessel function and show that it is an isomorphism between two suitably defined function spaces. The application of the $n$-dimensional bicomplex Hankel transform has been effectively demonstrated by solving some partial differential equations. Additionally, a new extension of coherent states is built based on the use of the bicomplex Bessel function and demonstrate that these states fulfill the conditions of normalizability, continuity and the resolution of unity.

math.CV↗

arXiv2024

Properties and applications of the Bicomplex Miller-Ross function

In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the bicomplex holomorphicity and Taylor series representation of this function are discussed, along with the derivation of a differential equation. Finally, as applications some relations of fractional order derivatives and solutions for the bicomplex extension of the generalized fractional kinetic equation involving the bicomplex Miller Ross function are derived.

math.CV↗

arXiv2023

Bicomplex generalized hypergeometric functions and their applications

In this work, generalized hypergeometric functions for bicomplex argument is introduced and its convergence criteria is derived. Furthermore, integral representation of this function has been established. Moreover, quadratic transformation, differential relation, analyticity and contiguous relations of this function are derived. Additionally, applications in quantum information system and quantum optics are provided as a consequence.

math.CV↗