Lucas sequences and Fibonacci numbers related equations. part i.: Differential equations and sums

Second order linear differential equation (LDE-2) y”+α(A,B)y’+β(A,B)y=0 has been set up, behaving approximately (an≈y(x=n)) and exactly (an= y(x=n)) to Lucas sequences (an = an-1 A+an-2 B) along with the note on the basic role of Fibonacci numbers among Lucas sequences. Certain sum rules (∑f(an) and...

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Bibliographic Details
Main Author: Kristyan, Sandor
Format: Conference Proceeding
Language:English
Subjects:
Differential equations
Fibonacci numbers
Mathematical analysis
Sum rules
Online Access:Get full text
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Summary:Second order linear differential equation (LDE-2) y”+α(A,B)y’+β(A,B)y=0 has been set up, behaving approximately (an≈y(x=n)) and exactly (an= y(x=n)) to Lucas sequences (an = an-1 A+an-2 B) along with the note on the basic role of Fibonacci numbers among Lucas sequences. Certain sum rules (∑f(an) and the fundamental ∑n=1Nan = a1+[(aN+1 − a2+B(aN-a1))(A+B-1)-1]) and its relation to complex function ez(n) are described. Compact formulae for ∑n=N[g(n) (h(nφ))m] are derived (g(x)= x or 1x, h(x)= sin(x) or cos(x), r>0, 0
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0081313