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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Mathematical… (More)

- V E Hogg Att, G L Alexanderson, bullet
- 2010

In the expansion (k-Dn (1+x+x 2 + .~ + x k-1 f = Y* [ / " ] * ' k>2, n> 0, 1=0 clearly For Ar = 2, these are the binomial coefficients and when dealing with these we shall use the usual notation: The problem of calculating sums of the following type for k = 2 was first treated by Cournot [2] and Ramus [5] and Ramus' method is outlined in [ 4 ] : N j=0 k… (More)

Graph theory almost certainly began when, in 1735, Leonhard Euler solved a popular puzzle about bridges. The East Prussian city of Königsberg (now Kalin-ingrad) occupies both banks of the River Pregel and an island, Kneiphof, which lies in the river at a point where it branches into two parts. There were seven bridges that spanned the various sections of… (More)

Gauss, in his work on quadratic reciprocity, defined in [1] an analogue to the binomial coefficients: n r i (x 1 1-D C x "-1-!) • • • (x n-k + 1-l) L k J (x k-l)(x k-X-!) • • • (x-1) ' n and k positive integers. In o r d e r to make the analogy to the binomial coefficients more complete, it is customary to let [!] • ' • for n = 0, 1, 2, • • • , and H-• for… (More)