Six Proofs for an Identity of the Lah Numbers
نویسنده
چکیده
In the paper, utilizing respectively the induction, a generating function of the Lah numbers, the Chu-Vandermonde summation formula, an inversion formula, the Gauss hypergeometric series, and two generating functions of Stirling numbers of the first kind, the authors collect and provide six proofs for an identity of the Lah numbers.
منابع مشابه
Inversions Relating Stirling, Tanh, Lah Numbers and an Application to Mathematical Statistics
Abstract. Inversion formulas have been found, converting between Stirling, tanh and Lah numbers. Tanh and Lah polynomials, analogous to the Stirling polynomials, have been defined and their basic properties established. New identities for Stirling and tangent numbers and polynomials have been derived from the general inverse relations. In the second part of the paper, it has been shown that if ...
متن کاملتأملی نو در نظریه عینیت ذات و صفات الهی
Critical investigation of Identity of essence and attributes of GodThe quality of the relationship between essence and attributes of God is one of the most important issues among islamic thinkers. One of the most important theories in this field is the theory of Identity of essence and attributes of God that divided in turn into two branches,I mean, external identification and conceptual ...
متن کاملInequalities of Ando's Type for $n$-convex Functions
By utilizing different scalar equalities obtained via Hermite's interpolating polynomial, we will obtain lower and upper bounds for the difference in Ando's inequality and in the Edmundson-Lah-Ribariv c inequality for solidarities that hold for a class of $n$-convex functions. As an application, main results are applied to some operator means and relative operator entropy.
متن کاملIRREDUCIBLE FACTORS OF THE q-LAH NUMBERS OVER Z
In this paper, we first give a new q-analogue of the Lah numbers. Then we show the irreducible factors of the q-Lah numbers over Z.
متن کاملTiling Proofs of Recent Sum Identities Involving Pell Numbers
In a recent note, Santana and Diaz–Barrero proved a number of sum identities involving the well–known Pell numbers. Their proofs relied heavily on the Binet formula for the Pell numbers. Our goal in this note is to reconsider these identities from a purely combinatorial viewpoint. We provide bijective proofs for each of the the electronic journal of combinatorics 13 (2006), #R00 1 results by in...
متن کامل