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!
|
| _version_ | 1832550226139807744 |
|---|---|
| author | Khristo N. Boyadzhiev |
| author_facet | Khristo N. Boyadzhiev |
| author_sort | Khristo N. Boyadzhiev |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8ae03ac0d45f41ad9d371bfeb8f9b9e2 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8ae03ac0d45f41ad9d371bfeb8f9b9e22025-02-03T06:07:18ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005233849386610.1155/IJMMS.2005.3849A series transformation formula and related polynomialsKhristo N. Boyadzhiev0Department of Mathematics, Ohio Northern University, Ada 45810, Ohio, USAWe 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.http://dx.doi.org/10.1155/IJMMS.2005.3849 |
| spellingShingle | Khristo N. Boyadzhiev A series transformation formula and related polynomials International Journal of Mathematics and Mathematical Sciences |
| title | A series transformation formula and related polynomials |
| title_full | A series transformation formula and related polynomials |
| title_fullStr | A series transformation formula and related polynomials |
| title_full_unstemmed | A series transformation formula and related polynomials |
| title_short | A series transformation formula and related polynomials |
| title_sort | series transformation formula and related polynomials |
| url | http://dx.doi.org/10.1155/IJMMS.2005.3849 |
| work_keys_str_mv | AT khristonboyadzhiev aseriestransformationformulaandrelatedpolynomials AT khristonboyadzhiev seriestransformationformulaandrelatedpolynomials |