Premium
Orthogonality via Transforms
Author(s) -
Freeman J. M.
Publication year - 1987
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1987772119
Subject(s) - orthogonality , mathematics , recursion (computer science) , sequence (biology) , degree (music) , function (biology) , polynomial , multiplication (music) , combinatorics , differential equation , pure mathematics , discrete mathematics , mathematical analysis , algorithm , physics , geometry , genetics , evolutionary biology , acoustics , biology
Let e ( x, t ) = ∑p n ( x ) t n be the generating function of a polynomial sequence, and the transform of multiplication by x relative to e ( x, t ). We show that the sequence p n ( x ) is orthogonal precisely when is a t ‐variable, i.e., maps K [ t ] into itself and increases degree by 1. We also show how transform techniques can shed light on the recursion relations and differential equations for p n ( x ).