TY - JOUR

T1 - Integration of Functions of a Hyperbolic Variable

AU - Luna-Elizarrarás, M. E.

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

KW - Functions of a hyperbolic variable

KW - Hyperbolic numbers

KW - Partial order

UR - http://www.scopus.com/inward/record.url?scp=85126748152&partnerID=8YFLogxK

U2 - 10.1007/s11785-022-01197-9

DO - 10.1007/s11785-022-01197-9

M3 - Artículo

AN - SCOPUS:85126748152

VL - 16

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

SN - 1661-8254

IS - 3

M1 - 35

ER -