Die Kombinationen gegebenen Profils. III
Differential equations associated with generalized Bell polynomials and their zeros
In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.
Divided differences and symmetric functions
L'operatore di differenze multivariate è utilizzato per stabilire varie formule di somme riguardanti le funzioni simmetriche, le quali hanno uno stretto legame con le identità del «termine costante».
Divisors, partitions and some new q-series identities
We obtain new q-series identities that have interesting interpretations in terms of divisors and partitions. We present a proof of a theorem of Z. B. Wang, R. Fokkink, and W. Fokkink, which follows as a corollary to our main q-series identity, and offer a similar result.
Duplicate inverse series relations and hypergeometric evaluations with
The Gould-Hsu (1973) inverse series relations have been systematically applied to the research of hypergeometric identities. Their duplicate version is established and used to demonstrate several terminating -summation formulas. Further hypergeometric evaluations with the same variable are obtained through recurrence relations.
ECO species.
Ein Beitrag zur Differenzrechnung und zur Zahlentheorie.
Einige kombinatorische Identitäten
Elementary proofs for convolution identities of Abel and Hagen-Rothe.
Elementary -identities. (Elementare -Identitäten.)
Énumération des permutations par nombre de marches
Equidistribution of descents, adjacent pairs, and place-value pairs on permutations.
Evaluation of a multiple integral of Tefera via properties of the exponential distribution.
Evaluations of some determinants of matrices related to the Pascal triangle.
Exact and asymptotic distributions in digital and binary search trees
Explicit enumeration of triangulations with multiple boundaries.
Exterior pairs and up step statistics on Dyck paths.
Falling factorials, generating functions, and conjoint ranking tables.
Finding the roots of polynomial equations: an algorithm with linear command.
We show how an old principle, due to Walsh (1922), can be used in order to construct an algorithm which finds the roots of polynomials with complex coefficients. This algorithm uses a linear command. From the very first step, the zero is located inside a disk, so several zeros can be searched at the same time.
Finite Rogers-Ramanujan type identities.