Abstract
In this chapter, we introduce the definition, properties, and theorems for the Legendre polynomials. We propose the supertrigonometric functions and superhyperbolic functions via Legendre polynomials. Moreover, we introduce the definitions, properties, and theorems for the Legendre-type polynomials. Finally, we discuss the supertrigonometric and superhyperbolic functions via Legendre-type polynomials.
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