The College of Education for Pure Sciences, Department of Mathematics, discussed a PhD thesis on homogeneous q-transformation effects and their applications.
q-polynomials and q-difference equations
The thesis presented by the researcher (Mahmoud Abdel Wahed Aref) included
Studying the homogeneous q-transformation operator we know the polynomials
(Rogers equation, inverse linear formula, generated function 1 and its expansion, as well as Miller's formula for polynomials ℎ
All of them have been demonstrated using the operator.
We focus on using the q-difference equations method to prove another generating function, the function
Homogenous q-difference equations and transformation formulas.
We know the homogeneous q-shift operator. Polynomials are described
new. We present the effect proof of the generating function and its expansion, formula
Rogers, Miller's Formula for Multiples
We use the q-difference equations method to prove another generative function, the expanded generative function, Rogers' formula and its expansion, Miller's formula, and the generative function of a type and transformation operator. We present Cauchy's general polynomials. We use Moth to create
Expanded Generator Function, Rogers Expanded Formula, and Miller's Formula for Polynomials
conclude the thesis
Rogers formula and the generating function of the polynomial
In addition, polynomials are introduced
And the smooth q-shift operator uses the operator
To prove and expand the generated function, Rogers' expanded formula
For Miller's formula for polynomials
Rogers formula for polynomials is derived.