Exponent generating functions of convolved generalized (p,q) numbers and symmetric functions

Abstract

In conclusion , we were able through this thesis to nd generating functions with an exponent (convolved), and generating functions of numbers of the fourth order with numbers of the third order, depending on the basic theorem in the third chapter, based on the results obtained in this thesis, we can get several new normal and exponential generating functions. Here are some possible suggestion : 1. Taking the alphabets A = fa1; a2; a3; a4g and E = fe1; e2; e3; e4g we suggest new theorem, so we can get the generating functions of the product of numbers and polynomials of fourth order. 2. Taking the alphabets E = fe1; e2; e3; e4; : : : ; ed+1g we suggest new theorem, so we can get d orthogonal polynomials. 3. Taking the alphabets A = fa1; a2; a3g, E = fe1; e2g and B = fb1; b2g we suggest new theorem, so we can get new results. 4. Taking the alphabets A = fa1; a2; a3g, E = fe1; e2; e3g and B = fb1; b2g we suggest new theorem, so we can get new results. 5. Taking the alphabets A = fa1; a2; a3g, E = fe1; e2; e3g and B = fb1; b2; b3g we suggest new theorem, so we can get new results. Also concerning the second chapter we suggest the form of convolved polynomials such as Mersenne polynomials, Pell polynomials,. . .