Lucas-Pantograph Type Exponential, Trigonometric, and Hyperbolic Functions
Ronald Orozco L\'opez
TL;DR
This paper introduces Lucas-Pantograph type exponential, trigonometric, and hyperbolic functions, along with their key identities, expanding the mathematical framework of Lucas calculus.
Contribution
It presents new Lucas-Pantograph functions and derives fundamental identities, enhancing the mathematical understanding of these functions.
Findings
Defined Lucas-Pantograph exponential functions
Established identities for Lucas-Pantograph trigonometric functions
Introduced Lucas-Pantograph hyperbolic functions
Abstract
In this paper, we include some new results for the Lucas calculus. A Lucas-Pantograph type exponential function is introduced. Additionally, we define Lucas-Pantograph type trigonometric functions, and some of their most notable identities are given: parity, sum and difference formulas, Pythagorean identities, double-angle identities, and some special values. Lucas-Pantograph type hyperbolic functions are also introduced.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Advanced Mathematical Theories · Mathematics and Applications