Portal de Periódicos da CAPES

Central factorials under the Kontorovich–Lebedev transform of polynomials

2012; Taylor & Francis; Volume: 24; Issue: 3 Linguagem: Inglês

10.1080/10652469.2012.672325

1476-8291

Ana F. Loureiro, Semyon Yakubovich,

Mathematical Analysis and Transform Methods

Abstract In this paper, we show that slight modifications of the Kontorovich–Lebedev (KL) transform lead to an automorphism of the vector space of polynomials. This circumstance along with the Mellin transformation property of the modified Bessel functions perform the passage of monomials to central factorial polynomials. A special attention is driven to the polynomial sequences whose KL transform is the canonical sequence, which will be fully characterized. Finally, new identities between the central factorials and the Euler polynomials are found. Keywords: central factorialsKontorovich–Lebedev transformmodified Bessel functionFourier transformLaguerre polynomialsHermite polynomialsEuler polynomialsBernoulli numbersEuler numbersGenocchi numbersStirling numberscombinatorial identitiesAMS Subject classification: 44A1533C1033C4511B6811B7311B8305A10 Acknowledgements Work of AFL is supported by Fundação para a Ciência e Tecnologia via the grant SFRH/BPD/63114/2009. This research is partially funded by the European Regional Development Fund through the programme COMPETE and by the Portuguese government through the FCT (Fundação para a Ciência e a Tecnologia) under the project PEst-C/MAT/UI0144/2011.