On an identity by Chaundy and Bullard - differnt proofs and generalizations (Dr. Michael Schlosser)
Sprache des Titels:
Englisch
Original Kurzfassung:
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, a notable special case by Ingrid Daubechies, while she was
setting up the theory of wavelets of compact support. We discuss a
number of different proofs of the identity, and explain its relationship
with Gauß hypergeometric series. We also consider the extension to
complex values of the two parameters which occur as summation bounds.
For a multivariable analogue of the identity, which was first given by
Damjanovic, Klamkin and Ruehr, we provide a new proof by splitting up
Dirichlet's multivariable beta integral. Finally, we present several
generalizations, including q- and elliptic extensions, of the
Chaundy-Bullard identity.
This is joint work with Tom Koornwinder.
Forschungs-