Integrating across Pascal's triangle
type: Item
instance of: scholarly article
title: Integrating across Pascal's triangle
zbMATH Open document ID: 1226.11026
author: Sam Northshield
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-11-22T00:00:00Z
full work available at URL: http://hdl.handle.net/1951/69918
review text: Using the Gamma function the author extends the binomial coefficients to real variables and proposes a continuous version of Pascal's triangle. Integration over various families of lines and curves yields quantities asymptotic to \(c^x\), where \(c\) is determined by the family and \(x\) is a parameter. Going back to the discrete case one obtains results on sums along curves. For example: \[ \limsup_{\sqrt{m^2+n^2}\to\infty}\binom{m+n}{m}^{\frac{1}{\sqrt{m^2+n^2}}}=2^{\sqrt{2}}. \]
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11B65
zbMATH DE Number: 5817863
zbMATH Keywords: Gamma function
zbMATH Keywords: binomial coefficients
zbMATH Keywords: Pascal's triangle
MaRDI profile type: Publication
OpenAlex ID: W2071924664
cites work: Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
cites work: Q3232397
cites work: Recurrent Sequences and Pascal's Triangle
cites work: Q3581839
cites work: Q3844537
DOI: 10.1016/J.JMAA.2010.09.018
description: scientific article; zbMATH DE number 5817863