Open AccessIdentities for linear recursive sequences of order <inline-formula><tex-math id="M1">$ 2 $</tex-math></inline-formula>
Author(s) -
Tian-Xiao He,
Peter J.-S. Shiue
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021049
Subject(s) - mathematics , order (exchange) , transformation (genetics) , polynomial , diophantine equation , discrete mathematics , combinatorics , arithmetic , mathematical analysis , genetics , biology , gene , finance , economics
We present here a general rule of construction of identities for recursive sequences by using sequence transformation techniques developed in [ 16 ]. Numerous identities are constructed, and many well known identities can be proved readily by using this unified rule. Various Catalan-like and Cassini-like identities are given for recursive number sequences and recursive polynomial sequences. Sets of identities for Diophantine quadruple are shown.