2000/07/13 by M. Mekhfi, Mekhfi, M.
Mathematics · Physics and Astronomy · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematical functions and polynomials #hep-th #math-ph #math.CA #math.FA #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0007017
8 pages latex
arxiv created 2000/07/13 · openalex publication_date 2000/07/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a recent paper we investigated the internal space of Bessel functions associated with their orders. We found a formula (new) unifying Bessel functions of integer and of real orders. In this paper we study the deformed exterior derivative system H=dλ on the puctured plane as a tentative to understand the origin of the formula and find that indeed similar formula occurs. This is no coincidence as we will demonstrate that generating functions of integer order Bessel functions and of real orders are respectively eigenstates of the usual exterior derivative and its deformation. As a direct consequence we rediscover the unifying formula and learn that the system linear in dλ is related to Bessel theory much as the system quadratic in (dλ+dλ*) is related to Morse theory.