Related papers: A master identity for Horadam numbers
We formulate several polynomial identities. One side of these identities has a nice simple form. Whereas the other has a form of a polynomial whose coefficients contain binomial coefficients double factorials or (and) rising factorials. The…
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
In this paper, we present a new approach to the convolved Fibonacci numbers arising from the generating function of them and give some new and explicit identities for the convolved Fibonacci numbers.
Two new identities about Catalan numbers are treated with Zeilberger's algorithm and Watson's hypergeometric series evaluation.
We evaluate some new three parameter families of finite reciprocal sums involving Horadam numbers. We will also be able to state the results for the infinite sums. Some Fibonacci and Lucas sums will be presented as examples.
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
In this note, we present several identities involving binomial coefficients and the two kind of Stirling numbers.
In the process of studying a conjecture of Holly M. Green and Martin W. Liebeck, we obtain two interesting identities by elementary methods, one is a combinatorial identity, and the other is a number theoretic identity.
Motivated by rigorous development in the theory of digamma functions, we have first derived some new identities for the digamma function, and then computed the values of digamma function for the fractional orders using these identities…
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
Using a specific form of the triple product identity, polygonal number identities are stated. Further number identities are examined that can be considered identities related to modular sets of numbers. The identities can be used to give…
By counting the numbers of periodic points of all periods for some interval maps, we obtain infinitely many new congruence identities in number theory.
This paper introduces a variation on an identity by Bruckman and Good. Using this identity, we are able to derive various well-known sums involving reciprocals of Fibonacci and Lucas numbers, including the case when the indices form an…
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…
We give alternative proof of Melham's and Howard's identities on generalised Fibonacci numbers
Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.
We present a differential-calculus-based method which allows one to derive more identities from {\it any} given Fibonacci-Lucas identity containing a finite number of terms and having at least one free index. The method has two {\it…
We propose and prove a new polynomial identity that implies Schur's partition theorem. We give combinatorial interpretations of some of our expressions in the spirit of Kur\c{s}ung\"oz. We also present some related polynomial and $q$-series…
We give new identities for some symmetric polynomials. As applications of these identities, we obtain some formulas for a higher order analogue of Fibonacci and Lucas numbers.
In a Hom-Malcev algebra an identity, equivalent to the Hom-Malcev identity, is found.