Central factorials under the Kontorovich-Lebedev transform of polynomials

Details Central factorials under the Kontorovich-Lebedev transform of polynomials Central factorials under the Kontorovich-Lebedev transform of polynomials

2011-10-27

arxiv.org/abs/1110.6015v2

Mathematics

Classical Analysis and ODEs

also available at http://cmup.fc.up.pt/cmup/ since the 2nd August 2011

Scientific paper

We show that slight modifications of the Kontorovich-Lebedev 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.

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