Open AccessOn a generalized function-to-sequence transform
Author(s) -
B. Slobodan Tričković,
Stanislav Stanković
Publication year - 2020
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm180908005t
Subject(s) - mathematics , bessel function , sequence (biology) , differential operator , operator (biology) , eigenfunction , inverse , hankel transform , mathematical analysis , eigenvalues and eigenvectors , pure mathematics , combinatorics , discrete mathematics , biochemistry , chemistry , genetics , physics , geometry , repressor , quantum mechanics , gene , transcription factor , biology
By attaching a sequence {?n}n?N0 to the binomial transform, a new operator D? is obtained. We use the same sequence to define a new transform T? mapping derivatives to the powers of D?, and integrals to D-1?. The inverse transform B? of T? is introduced and its properties are studied. For ?n = (-1)n, B? reduces to the Borel transform. Applying T? to Bessel's differential operator d/dx x d/dx, we obtain Bessel's discrete operator D?nN?. Its eigenvectors correspond to eigenfunctions of Bessel's differential operator.