An Integral Representation Formula for Multi Meta- φ -Monogenic Functions of Second Class

Consider the following operator (Formula presented.)where φ^(j) is a Clifford-valued function and λ^(j) is a Clifford-constant defined by (Formula presented.) with m= m₁+ ⋯ + m_n, a₁= m₀= 0 and a_j= m₁+ ⋯ + m_{j- 1} for j= 2 , … , n; and φi(j) can be real-valued functions defined in Rm1+1×Rm2+1×⋯×Rmn+1. λi(j) are real numbers for i= 0 , 1 , … , m_j and j= 1 , … , n. A function u is multi meta- φ-monogenic of second class, in several variables x^(j), for j= 1 , … , n, if Dφ(j),λ(j)u=0.In this paper we give a Cauchy-type integral formula for multi meta-φ-monogenic of second class operator in one way by iteration and in the second way by the use of the construction of the Levi function. Also, in this work, we define a multi meta-φ-monogenic function of first class with the help of the Clifford type algebras depending on parameters.