On the multiplicative Legendre equation

Abstract

When exponentials are employed to model procedures and efficacies appearing in real life, an additive derivative of this type of function does not exist. From this perspective, we define the Legendre equation in multiplicative analysis by several algebraic structures. Multiplicative Legendre polynomials of constituted problem are obtained by the power series solution method. Moreover, for the multiplicative Legendre equation, the generating function is obtained, and an integral presentation is constructed. Eventually, some fundamental spectral features of the multiplicative Legendre problem are analysed.

Keywords

• Legendre equation
• multiplicative calculus
• multiplicative Sturm-Liouville equation
• non-Newtonian calculus
• 44A15
• 11N05