Operational Methods in the Study of Sobolev-Jacobi Polynomials

• DOI: 10.3390/math7020124
• Publication Date: 2019-01-24T16:12:48Z
• Authors: Nicolas Behr; Giuseppe Dattoli; Gérard H. E. Duchamp; Silvia Licciardi; Karol A. Penson
• Keywords: Lacunary function; Laguerre polynomials

Inspired by ideas from umbral calculus and based on the two types of integrals occurring in defining equations for gamma reciprocal functions, respectively, we develop a multi-variate version so-called image technique. Besides providing class new formulae generalized hypergeometric functions an implementation series manipulations computing lacunary generating our main application these techniques is study Sobolev-Jacobi polynomials. Motivated applications to theoretical chemistry, moreover present deep link between normal-ordering introduced Gurappa Panigrahi, two-variable Hermite polynomials integral-based transforms. Notably, thus calculate all K-tuple L-shifted exponential certain family (SJ) explicitly.