Operational Methods in the Study of Sobolev-Jacobi Polynomials
AbstractInspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-called umbral image technique. Besides providing a class of new formulae for generalized hypergeometric functions and an implementation of series manipulations for computing lacunary generating functions, our main application of these techniques is the study of Sobolev-Jacobi polynomials. Motivated by applications to theoretical chemistry, we moreover present a deep link between generalized normal-ordering techniques introduced by Gurappa and Panigrahi, two-variable Hermite polynomials and our integral-based series transforms. Notably, we thus calculate all K-tuple L-shifted lacunary exponential generating functions for a certain family of Sobolev-Jacobi (SJ) polynomials explicitly. View Full-Text
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Behr, N.; Dattoli, G.; Duchamp, G.H.E.; Licciardi, S.; Penson, K.A. Operational Methods in the Study of Sobolev-Jacobi Polynomials. Mathematics 2019, 7, 124.
Behr N, Dattoli G, Duchamp GHE, Licciardi S, Penson KA. Operational Methods in the Study of Sobolev-Jacobi Polynomials. Mathematics. 2019; 7(2):124.Chicago/Turabian Style
Behr, Nicolas; Dattoli, Giuseppe; Duchamp, Gérard H.E.; Licciardi, Silvia; Penson, Karol A. 2019. "Operational Methods in the Study of Sobolev-Jacobi Polynomials." Mathematics 7, no. 2: 124.
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