Mathematics – Classical Analysis and ODEs
Scientific paper
2007-12-13
Indag. Math. (N.S.) 19 (2008), 239-261
Mathematics
Classical Analysis and ODEs
20 pages; added in v3: more references to earlier occurrences of the identity and its multivariable analogue, combinatorial pr
Scientific paper
An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. This identity was rediscovered many times. Notably, a special case was rediscovered by I. Daubechies, while she was setting up the theory of wavelets of compact support. We discuss or survey many different proofs of the identity, and also its relationship with Gauss hypergeometric series. We also consider the extension to complex values of the two parameters which occur as summation bounds. The paper concludes with a discussion of a multivariable analogue of the identity, which was first given by Damjanovic, Klamkin and Ruehr. We give the relationship with Lauricella hypergeometric functions and corresponding PDE's. The paper ends with a new proof of the multivariable case by splitting up Dirichlet's multivariable beta integral.
Koornwinder Tom H.
Schlosser Michael J.
No associations
LandOfFree
On an identity by Chaundy and Bullard. I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On an identity by Chaundy and Bullard. I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On an identity by Chaundy and Bullard. I will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-622886