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Integration of Functions of a Hyperbolic Variable

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Abstract

This paper presents a systematic study of the theory of integration of hyperbolic-valued functions from a new point of view where the notion of partial order defined on the set of hyperbolic numbers and the notion of hyperbolic intervals have been taken into consideration. Starting with the definitions of partition of a hyperbolic interval and the definition of hyperbolic integral, the basic theorems of hyperbolic integration are proved, thus establishing a solid foundation of a theory that allows further developments.

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  1. Department of Mathematics, Holon Institute of Technology, 52 Golomb St., P.O.B. 305, 5810201, Holon, Israel

    M. E. Luna-Elizarrarás

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  1. M. E. Luna-Elizarrarás
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Correspondence to M. E. Luna-Elizarrarás.

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Communicated by Fabrizio Colombo.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

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Luna-Elizarrarás, M.E. Integration of Functions of a Hyperbolic Variable. Complex Anal. Oper. Theory 16, 35 (2022). https://doi.org/10.1007/s11785-022-01197-9

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