Abstract
We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus M(r;f) satisfies 1n M(r;f) ≤A 1n2 r. This solves the problem of constructing such entire functions from their values at [aqn + q-n /a]/2, for 0<q<1. Our technique is constructive and gives an explicit representation of the sought entire function. Applications to q-series identities are given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 125-146 |
| Number of pages | 22 |
| Journal | Journal of Approximation Theory |
| Volume | 123 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 1 2003 |
Keywords
- Askey-Wilson operators
- Carlson's theorem
- Integral representations
- Polynomial bases
- q-Taylor series
- q-exponential function