Lucas-Pantograph Type Exponential, Trigonometric, and Hyperbolic Functions

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.