𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Extension of a result of ainsworth and liu

✍ Scribed by Henry E. Fettis

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
88 KB
Volume
316
Category
Article
ISSN
0016-0032

No coin nor oath required. For personal study only.

✦ Synopsis

As an incidental result of a study by Ainsworth and Liu (l), the following identity was obtained : s ' (l-~)~ ln(l-x)P,_,(x)dx = 2P( -l)p+"[(p-l)!]"(n-p-l)! (n+p-l)! ( 1)

where P,_ 1(x) is the Legendre polynomial of degree (n -l), and p is an integer such that 1 d p < n. However, since the integral in ( 1) exists for all p with Re(p) > 0, it appears that a result extending the range of p to all values in the R.H.P. should also be of interest. This may be accomplished by starting with the known relation (2), itself valid for Re(p) > 0:

πŸ“œ SIMILAR VOLUMES

Extension of a clique cover result to un
Extension of a clique cover result to uniform hypergraphs
✍ A. Patricia Shelton; Ronald D. Dutton; Robert C. Brigham πŸ“‚ Article πŸ“… 1986 πŸ› Elsevier Science 🌐 English βš– 137 KB

An r-uniform hypergraph is a structure H = (V, E), where V is a set of nodes and E is a collection of subsets of the nodes, called edges, each of which has size r. H is complete with p I> r nodes if it has all possible (~) edges and is empty if it has no edges. The complement of H is the r-uniform h

Extensions of Gallai–Ramsey results
Extensions of Gallai–Ramsey results
✍ Shinya Fujita; Colton Magnant πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 246 KB

## Abstract Consider the graph consisting of a triangle with a pendant edge. We describe the structure of rainbow ‐free edge colorings of a complete graph and provide some corresponding Gallai–Ramsey results. In particular, we extend a result of Gallai to find a partition of the vertices of a rain