Open AccessA Study on the Sum of the Squares of Generalized p-Oresme Numbers: The Sum Formula \(\sum{^n_k{_=}{_0}}x^kW{^2_m{_k}_+{_j}}\)
Author(s) -
Yüksel Soykan
Publication year - 2022
Publication title -
asian journal of advanced research and reports
Language(s) - English
Resource type - Journals
ISSN - 2582-3248
DOI - 10.9734/ajarr/2022/v16i130444
Subject(s) - mathematics , mathematical proof , combinatorics , explained sum of squares , sums of powers , mathematical induction , sum rule in quantum mechanics , discrete mathematics , physics , statistics , geometry , quantum mechanics , quantum chromodynamics
In this paper, closed forms of the sum formulas \(\sum{^n_k{_=}{_0}}x^kW{^2_m{_k}_+{_j}}\) for generalized p-Oresme numbers are presented. As special cases, we give sum formulas of Modified p-Oresme, p-Oresme-Lucas and p-Oresme numbers. We present the proofs to indicate how these formulas, in general, were discovered. Of course, all the listed formulas may be proved by induction, but that method of proof gives no clue about their discovery.