Moment-based methods are used to generate the three-term recurrence relation for polynomials orthogonal with respect to the Prudnikov, the generalized Prudnikov, and Prudnikov-type weight functions and their symmetric extensions. All procedures developed are implemented, and made available, in MATLAB software.
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Brychkov, Yu.A., Marichek, A.O.I., Savischenko, N.V.: Handbook of Mellin transforms, Advances in Applied Mathematics. CRC Press, Boca Raton (2019)
Coussement, E., Van Assche, W.: Properties of multiple orthogonal polynomials associated with Macdonald functons. Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications (Patras, 1999). J. Comp. Appl. Math. 133, 253–261 (2001)
Gautschi, W.: Orthogonal polynomials in MATLAB. Exercises and Solutions, Software, Environments and Tools, 26. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2016)
Gautschi, W.: A software repository for orthogonal polynomials, Software, Environments and Tools 28. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2018)
Gordon, R.G.: Constructing wavefunctions for nonlocal potentials. J. Chem. Phys. 52, 6211–6217 (1970)
Olver, F.W.J., et al. (eds.): NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge (2010)
Van Assche, W.: Open problems. Proceedings of the Seventh Spanish Symposium on Orthogonal Polynomials and Applications (VII SPOA) (Granada 1991). J. Comput. Appl. Math. 48, 225–243 (1993)
Van Assche, W., Yakubovich, S.B.: Multiple orthogonal polynomials associated with Macdonald functions. Integral Transform. Spec. Funct. 9, 229–244 (2000)
Walter, G: A software repository for Gaussian quadratures and Christoffel functions, Software, Environments and Tools, 32. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2021)
Yakubovich, S.: Orthogonal polynmials with the Prudnikov-type weights. Complex Anal. Oper. Theory 14(1), Art. 26, pp. 27 (2020)
Yakubovich, S.: Orthogonal polynomials with ultra-exponential weight functions An explicit solution to the Ditkin–Prudnikov problem. Constr. Approx. 53, 1–38 (2021)
Zhang, L.: A note on the limiting mean distribution of singular values for products of two Wishart random matrices. J. Math. Phys. 54(8), 083303, 8 (2013)
The work of the second author was supported in part by the Serbian Academy of Sciences and Arts (Φ-96).
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Gautschi, W., Milovanović, G.V. Orthogonal polynomials relative to weight functions of Prudnikov type. Numer Algor (2021). https://doi.org/10.1007/s11075-021-01187-6
- Orthogonal polynomials
- Prudnikov-type weight functions
- Three-term recurrence relation
Mathematics Subject Classification (2010)