Two Classes of Special Functions Using Fourier Transforms of Some Finite Classes of Classical Orthogonal Polynomials
نویسندگان
چکیده
Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by exp(−x2/2), which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences.
منابع مشابه
Two Finite Classes of Orthogonal Functions
By using Fourier transforms of two symmetric sequences of finite orthogonal polynomials, we introduce two new classes of finite orthogonal functions and obtain their orthogonality relations via Parseval’s identity.
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