Dear Hadi Roopaei

The difference due to the different entries, but both based on gamma function.

That is Cesaro Matrix C = cij

is defined by the enrtries

cij= (Ai-j )^{α-1})/(Ai^{α}), where

Ai^{α} = Γ(i+α+1)/Γ(α+1)Γ(i+1), Γ is gamma function.

Where the generalized p - Cesaro Matrix has the entries

(Ai^{α}, p)ij = (Γ(i+α+1)/Γ(i-j+1)Γ(j+α+1)) × (pΓ(j+α+1)Γ(i-j+p)/Γ(i+α+p+1))

Remark: There are other generalizations.

Best regards

Dear Hadi Roopaei

I observed that you have a publication in the same domain.

https://www.tandfonline.com/doi/abs/10.1080/03081087.2018.1501330?journalCode=glma20

" Factorization of Cesàro and Hilbert matrices based on generalized Cesàro matrix "

This shows that you know the answer to your question.

Is this a matter of advertisement?

Dear Issam

Yes I know the answer of my question and attached it as well. I put that question in this site because many mathematicians do not know the differences of these operators. I have also a bad experience that a referee of one of my papers rejected my paper just 2 days after the submission day only because he did not know these matrices differences . For this reason I propose this question in the RG.

Thanks for kind reply