Results 31 to 40 of about 54,116 (276)
Combinatorial Proofs of Identities of Alzer and Prodinger and Some Generalizations [PDF]
, 2018 We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have Our ...
Engbers, John, Stocker, Christopher
core +1 more source
On some combinatorial identities and harmonic sums
, 2017 For any $m,n\in\mathbb{N}$ we first give new proofs for the following well known combinatorial identities \begin{equation*} S_n(m)=\sum\limits_{k=1}^n\binom{n}{k}\frac{(-1)^{k-1}}{k^m}=\sum\limits_{n\geq r_1\geq r_2\geq...\geq r_m\geq 1}\frac{1}{r_1r_2 ...
Batir, Necdet
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Blinatumomab has been shown to be highly effective for patients with pediatric B‐ALL and has recently become standard of care therapy. Due to its past use in the clinical trial setting, there is limited information available about real‐world administration.
Katelyn Oranges +12 more
wiley +1 more source
Combinatorial Identities for the Narayana Numbers
AxiomsWe interpret the Narayana numbers combinatorially by having them count the number of tilings of an n-strip using squares and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Narayana numbers ...
Ángel Plaza, Steven J. Tedford
doaj +1 more source
Combinatorial Identities for Incomplete Tribonacci Polynomials [PDF]
, 2014 The incomplete tribonacci polynomials, denoted by T_n^{(s)}(x), generalize the usual tribonacci polynomials T_n(x) and were introduced in [10], where several algebraic identities were shown.
Shattuck, Mark
core +2 more sources
Partition Identities for Ramanujan's Third Order Mock Theta Functions
, 2010 We find two involutions on partitions that lead to partition identities for Ramanujan's third order mock theta functions $\phi(-q)$ and $\psi(-q)$. We also give an involution for Fine's partition identity on the mock theta function f(q).
Chen, William Y. C. +2 more
core +1 more source
Pediatric Blood &Cancer, EarlyView.ABSTRACT Objective To evaluate selumetinib exposure using therapeutic drug monitoring (TDM) in pediatric patients with neurofibromatosis type 1 (NF1) and plexiform neurofibromas (PN), assess interpatient pharmacokinetic variability, and explore the relationship between drug exposure, clinical response, and adverse effects.
Janka Kovács +8 more
wiley +1 more source
Some Properties of the (p,q)-Fibonacci and (p,q)-Lucas Polynomials
Journal of Applied Mathematics, 2012 Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper we consider the Pascal matrix and define a new generalization of Fibonacci polynomials ...
GwangYeon Lee, Mustafa Asci
doaj +1 more source
Proofs of some binomial identities using the method of last squares [PDF]
, 2010 We give combinatorial proofs for some identities involving binomial sums that have no closed form.Comment: 8 pages, 16 ...
Shattuck, Mark, Waldhauser, Tamás
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Pediatric Blood &Cancer, EarlyView.ABSTRACT Arteriovenous malformations (AVMs) are rare, high‐flow, vascular anomalies that can occur either sporadically or as part of a genetic syndrome. AVMs can progress with serious morbidity and even mortality if left unchecked. Sirolimus is an mTOR inhibitor that is effective in low‐flow vascular malformations; however, its role in AVMs is unclear.
Will Swansson +3 more
wiley +1 more source