Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Note on the binomial partial difference equation
Journal: Electronic Journal of Qualitative Theory of Differential Equations
Volume: 2015
Issue Date: 1-Jan-2015
Rank: M21
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2015.1.96
Some formulas for the “general solution” to the binomial partial difference equation cm,n = cm-1,n + cm-1,n-1, are known in the literature. However, it seems that there is no such a formula on the most natural domain connected to the equation, that is, on the set (Formula Presented) By using a connection with the scalar linear first order difference equation we show that the equation on the domain D\{(0, 0)}, can be solved in closed form by presenting a formula for the solution in terms of the “side” values (Formula Presented).
Keywords: Binomial coefficients | Equation solvable in closed form | Partial difference equation
Publisher: Bolyai Institute, University of Szeged
Project: Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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