Corpus ID: 59409668

ONE PARAMETER GENERALIZATIONS OF THE FIBONACCI AND LUCAS NUMBERS

@article{Ismail2008ONEPG,
  title={ONE PARAMETER GENERALIZATIONS OF THE FIBONACCI AND LUCAS NUMBERS},
  author={M. Ismail},
  journal={arXiv: Classical Analysis and ODEs},
  year={2008}
}
  • M. Ismail
  • Published 2008
  • Mathematics
  • arXiv: Classical Analysis and ODEs
We give one parameter generalizations of the Fibonacci and Lucas numbers denoted by {Fn(�)} and {Ln(�)}, respectively. We evaluate the Hankel determinants with entries {1/Fj+k+1(�) : 0 � i,jn} and {1/Lj+k+1(�) : 0 � i,jn}. We also find the entries in the inverse of {1/Fj+k+1(�) : 0 � i,jn} and show that all its entries are integers. Some of the identities satisfied by the Fibonacci and Lucas numbers are extended to more general numbers. All integer solutions to three diophan- tine equtions… Expand
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References

SHOWING 1-10 OF 21 REFERENCES
INVERSE TRIGONOMETRIC AND HYPERBOLIC SUMMATION FORMULAS INVOLVING GENERALIZED FIBONACCI NUMBERS
  • 14
  • PDF
Fibonacci numbers and orthogonal polynomials
  • 23
  • Highly Influential
  • PDF
The Filbert Matrix
  • 34
  • PDF
Fibonacci and Lucas Numbers
  • 250
  • PDF
Fibonacci and Lucas Numbers with Applications
  • 1,039
  • Highly Influential
TRICKS OR TREATS WITH THE HILBERT MATRIX
  • 145
Basic Hypergeometric Series
  • 2,555
JR 旅客販売総合システム(マルス)における運用及び管理について
  • 15,099
  • Highly Influential
  • PDF
...
1
2
3
...