Wyniki wyszukiwania - BazTech

1

Two-parametric quasi-Fibonacci numbers

Smoleń B., Wituła R.

Silesian Journal of Pure and Applied Mathematics

|

2017

|

Vol. 7, iss. 1

99--121

EN

This paper is devoted to the discussion on the two parametric quasi–Fibonacci numbers. The fundamental recurrence and reduction formulae for arguments and indices of these quasi–Fibonacci numbers are presented here. The matrix representations of the considered numbers are described and their applications are indicated. Moreover, a number of connections of the two parametric quasi-Fibonacci numbers with the sequences collected in the OEIS encyclopaedia are noted. Despite quite large volume of this elaboration, the Authors believe that this is just some kind of announcement, or an introduction to a definitely larger and detailed discussion including, above all, the applications of the investigated here numbers.

2

On values of the psi function

Adam M., Piątek B., Pleszczyński M., Smoleń B., Wituła R.

Journal of Applied Mathematics and Computational Mechanics

|

2017

|

Vol. 16, nr 1

7--18

EN

In the present paper, values of the psi function for many arguments connected with the golden ratio and Fibonacci numbers are determined or given in alternative form. Moreover, some integral representation of the psi function is found. This is a potential calculation base of values of the psi function for powers of argument. We also note that this integral representation gives better numerical estimation of values of the psi function than the respective Legendre’s integral formula.

3

Certain inequalities connected with the golden ratio and the Fibonacci numbers

Adam M., Piątek B., Pleszczyński M., Smoleń B., Wituła R.

Journal of Applied Mathematics and Computational Mechanics

|

2016

|

Vol. 15, nr 1

5--15

EN

In the present paper we give some condensation type inequalities connected with Fibonacci numbers. Certain analytic type inequalities related to the golden ratio are also presented. All results are new and seem to be an original and attractive subject also for future research.