24 research outputs found
On the Harmonic and Hyperharmonic Fibonacci Numbers
In this paper, we study the theory of the harmonic and the hyperharmonic
Fibonacci numbers. Also, we get some combinatoric identities like as harmonic
and hyperharmonic numbers and we obtain some useful formulas for
, which is finite sums of reciprocals of Fibonacci numbers. We
obtain spectral and Euclidean norms of circulant matrices involving harmonic
and hyperharmonic Fibonacci numbers
Investigating Exponential and Geometric Polynomials with Euler-Seidel Algorithm
In this paper we use Euler-Seidel matrices method to find out some properties
of exponential and geometric polynomials and numbers. Some known results are
reproved and some new results are obtained.Comment: 12 page
Polynomials Related to Harmonic Numbers and Evaluation of Harmonic Number Series I
In this paper we focus on two new families of polynomials which are connected
with exponential polynomials and geometric polynomials. We discuss their
generalizations and show that these new families of polynomials and their
generalizations are useful to obtain closed forms of some series related to
harmonic numbers.Comment: 18 page
Extended Bernoulli and Stirling matrices and related combinatorial identities
In this paper we establish plenty of number theoretic and combinatoric
identities involving generalized Bernoulli and Stirling numbers of both kinds.
These formulas are deduced from Pascal type matrix representations of Bernoulli
and Stirling numbers. For this we define and factorize a modified Pascal matrix
corresponding to Bernoulli and Stirling cases.Comment: Accepted for publication in Linear Algebra and its Application
Polynomials with r-Lah coefficient and hyperharmonic numbers
In this paper, we take advantage of the Mellin type derivative to produce
some new families of polynomials whose coefficients involve r-Lah numbers. One
of these polynomials leads to rediscover many of the identities of r-Lah
numbers. We show that some of these polynomials and hyperharmonic numbers are
closely related. Taking into account of these connections, we reach several
identities for harmonic and hyperharmonic numbers