There is only a little passage in WWikipedia (https://en.wikipedia.org/wiki/Orthogonal_polynomials) about the history of orthogonal polynomials, namely: "The field of orthogonal polynomials developed in the late 19th century from a study of continued fractions by P. L. Chebyshev and was pursued by A. A. Markov and T. J. Stieltjes. Some of the mathematicians who have worked on orthogonal polynomials include Gábor Szegő, Sergei Bernstein, Naum Akhiezer, Arthur Erdélyi, Yakov Geronimus, Dave Gwyn, Wolfgang Hahn, Theodore Seio Chihara, Mourad Ismail, Waleed Al-Salam, and Richard Askey." I would like to known more details about how this theory and the theory of orthogonal functions envolved along the centuries, but I did not find any reference. Any comments will be appreciated.
Best,
Ricardo.
The book by Giovanni Sansone
Giovanni Sansone: Orhogonal functions, Interscience Inc. 1951, Dover 1991, 2004, ISBN 978-0486667300
does not present the story of the topic, but contains a bibliography with references to all the key works and papers of the second half of the 19th century and early 20th century, so it may be useful for you.
The following are some Books involving certain historical information about orthogonal polynomials and function.
http://b-ok.xyz/book/571422/19dfc0
http://b-ok.xyz/book/611404/7d47e5
http://b-ok.xyz/book/869678/e2f477
http://b-ok.xyz/book/2373238/2e3b8d
http://b-ok.xyz/book/3101910/fb76a3
But I have not seen yet any book specialized in the history of orthogonal polynomials and functions.
Thank you Luca Bonaventura and Maged Bin-Saad. I will look to the references you indicate me. Best Regards. Ricardo.
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