A series transformation formula and related polynomials
We present a formula that turns power series into series of functions. This formula serves two purposes: first, it helps to evaluate some power series in a closed form; second, it transforms certain power series into asymptotic series. For example, we find the asymptotic expansions for λ>0 of the...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2005-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3849 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We present a formula that turns power series into series of
functions. This formula serves two purposes: first, it helps to
evaluate some power series in a closed form; second, it transforms
certain power series into asymptotic series. For example, we find
the asymptotic expansions for λ>0 of the incomplete gamma function γ(λ,x) and of the Lerch transcendent Φ(x,s,λ). In one particular case, our formula reduces
to a series transformation formula which appears in the works of
Ramanujan and is related to the exponential (or Bell) polynomials.
Another particular case, based on the geometric series, gives rise
to a new class of polynomials called geometric polynomials. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |