I am searching for a good book in orthogonal polynomials (for good I mean detailed and with all the basic results one has to know before doing some research in that branch ) for beginners ( nothing at all in that area of math)
So Can someone give me some recommendations?
Thanks in advance.
I am not sure if there is a single book that covers all the material for the beginners. This is simply because there are different research groups with different focus.
Theodore Chihara's book "An Introduction to Orthogonal Polynomials" may be what you are looking for.
In connection with potential theory I can suggest a survey titled "Orthogonal polynomials" by Vilmos Totik: link
Spectral theory related part can be found in "SPECTRAL THEORY AND SPECIAL FUNCTIONS" by Erik Koelink: link
There is also an algebraic aspect of the theory for which I am not qualified to suggest a good reference book or article.