| Title:
|
A function related to the central limit theorem (English) |
| Author:
|
Bracken, Paul |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
765-775 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A number of properties of a function which originally appeared in a problem proposed by Ramanujan are presented. Several equivalent representations of the function are derived. These can be used to evaluate the function. A new derivation of an expansion in inverse powers of the argument of the function is obtained, as well as rational expressions for higher order coefficients. (English) |
| Keyword:
|
series |
| Keyword:
|
Ramanujan |
| MSC:
|
11B83 |
| MSC:
|
32A05 |
| MSC:
|
33B10 |
| idZBL:
|
Zbl 1059.33500 |
| idMR:
|
MR1715465 |
| . |
| Date available:
|
2009-01-08T18:48:28Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119051 |
| . |
| Reference:
|
[1] Ramanujan S.: Question 294.J. Indian Math. Soc. 3 , 128 (1911). |
| Reference:
|
[2] Ramanujan S.: On Question 294.J. Indian Math. Soc. 4 , 151 (1912). |
| Reference:
|
[3] Berndt B.C.: Ramanujan's Notebooks.Vol II, Springer, 1985. Zbl 0944.01005, MR 0781125 |
| Reference:
|
[4] Bowman K.O., Shenton L.R., Szekeres G.: .J. Stat. Comput. Siml. 20 , 167 (1984). |
| Reference:
|
[5] Copson E.T.: An Introduction to the Theory of Functions of a Complex Variable.Clarendon Press, Oxford, 1970. Zbl 0188.37901 |
| . |
