A Panorama of Hungarian Mathematics in the Twentieth Century I

Volume 14 of the series Bolyai Society Mathematical Studies pp 55-70

Orthogonal Polynomials

  • József SzabadosAffiliated withAlfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences

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The theory of orthogonal polynomials plays an important role in many branches of mathematics, such as approximation theory (best approximation, interpolation, quadrature), special functions, continued fractions, differential and integral equations. The notion of orthogonality originated from the theory of continued fractions, but later became an independent (and possibly more important) discipline. Among the contributors to the theory of orthogonal polynomials, we can find such outstanding mathematicians as Abel, Chebyshev, Fourier, Hermite, Laguerre, Laplace, Legendre, Markov, and Stieltjes, just to name a few. Beginning with Gábor Szegő, Hungarian mathematicians like Pál Erdös, Pál Turán, Géza Freud, Ervin Feldheim and others have made essential contributions to the flourishing theory of orthogonal polynomials in the last century. At this point I would like to mention two names who have made considerable efforts to propagate the work of the above mentioned Hungarian mathematicians: Richard Askey and Doron Lubinsky.