On a generalized function-to-sequence transform | Zendy

Slobodan B. Tričković | Zendy; Miomir S. Stanković | Zendy

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On a generalized function-to-sequence transform

Author(s) -

Slobodan B. Tričković,

Miomir S. 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.

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