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Closed Formulas for Singly‐Periodic Monogenic Cotangent, Cosecant and Cosecant‐Squared Functions in Clifford Analysis
Author(s) -
Constales D.,
Kraußhar R. S.
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702004003
Subject(s) - trigonometric functions , mathematics , trigonometry , dimension (graph theory) , mathematical analysis , pure mathematics , inverse trigonometric functions , bounded function , fourier series , geometry
Singly‐periodic monogenic cotangent and cosecant functions are important to Clifford analysis because they are the building blocks of the Bergman and Szegö reproducing kernels for strip domains, that is, rectangular domains with a single bounded dimension. The paper establishes a wide range of explicit formulas for these functions, in terms of derivatives, of one‐dimensional integrals, and of Fourier and plane wave multidimensional integrals. These results indicate how the elementary trigonometric functions cot( z ), csc( z ) and csc 2( z ) are ramified into different entities when the setting is switched from complex analytic to Clifford monogenic.